A Google Books search for "professional bias" for the period 1700–1800 yields four legitimate matches—all of them connected to religion. From Richard Watson, An Apology for Christianity in a series of Letters, Addressed to Edward Gibbon, Esq (1777):
I beg pardon for styling their [the Deists'] reasoning, prejudice ; I have no design to give offence by that word ; they may, with equal right, throw the same imputation upon mine ; and I think it just as illiberal in Divines, to attribute the scepticism of every Deist to wilful infidelity; as it is in the Deist, to refer the faith of every Divine to professional bias.
Bishop Watson's response to Gibbon is cited in Letter 44 of Richard Sullivan, A View of Nature, in Letters to a Traveller Among the Alps (1794):
A latent, and even involuntary scepticism, certainly adheres to some characters. And therefore, it is illiberal in the advocates of religion, to attribute the scepticism of every Deist to perverse infidelity ; as it is in the Deists, to refer the faith of every Christian to professional bias.* This particular bent we can neither comprehend, nor estimate.
*Bishop Watson.
As Hot Licks notes in a comment below, this is by no means an independent occurrence of "professional bias," but rather a restatement of the previous instance, with Christian substituted for Divine.
From a letter to the Philological Society of London by N. N. on March 7, 1787, in The European Magazine (March 1787):
We have a hint also of "the number and ability of unbelievers." I will not class the Reviewer with those Free-thinkers, as they call themselves, who are mere slaves to the opinion of others ; though I suspect him to have very little knowledge of the facts or answers in defence of Christianity. With those, however, who disbelieve, not from any reason they themselves can give, but because some acquaintance of theirs, of whom they have a good opinion, or some celebrated writer, as Voltaire, Hume, disbelieved, we may argue in their own way, and confront them with names and authority, I trust, superior to any they can produce. ... To say nothing therefore of the bulk of the community, high and low, rich and poor, learned and illiterate, which or so many ages have believed in the Gospel, let us only urge the names of Mede, Cudworth, Barrow, Clarke, Jortin, ; of Leland, Taylor, Lardner ; of Le Clerc, Limborch, Mosheim ; men who spent whole lives in the study of Christianity, and manifested as much freedom and acuteness in their researches, as are to be found in any science whatever. Let us add the authority of Bacon, Grotius, Locke, Newton, Hartley, men who were under no professional bias, and did not take their religion upon trust, but each of them spent many years in inquiries into it, and rose up from the inquiry fully and firmly persuaded of its truth.
And from The Parliamentary Register (April 28, 1795):
The Bishop of ROCHESTER disclaimed having any professional bias : he said, in all great bodies of men there were some undeserving objects, but it would be unjust to punish the worthy on their account.
As two of the four eighteenth-century instances of "professional bias" in the Google Books search results are from bishops, a third quotes one of the first two, and the fourth distinguishes between "men who spent whole lives in the study of Christianity" and men who merely "spent many years in inquiries into it" (arguing that the latter did not have a professional bias), it seems clear that prior to the 1800s the term was understood to refer to religious profession.
The earliest nonreligious (or religion-neutral) instance of "professional bias" in a Google Books search appears in a review of John Fuller, M.D., The History of Berwick upon Tweed, in The Monthly Review (October 1800):
This design [to improve "the present state of agriculture and commerce of his native town" and to propose "the real happiness of the inhabitants"] is no doubt truly benevolent and patriotic : but surely it was not necessary, in order to impress on the reader's mind the importance and utility of agriculture, to give an account of man in a savage state ; nor to present us with various other observations which here occur, and which seem to originate in the professional bias of the author's ideas.
Since the author is a medical doctor and not a divine, I assume that his professional bias is in the direction of modern medicine. The review doesn't mention religion at all.
This rather limited record supports the idea that "professional bias" began as a term connected to the profession (that is to say, the professing) of Christianity and used by various religious and nonreligious writers, and that from there it expanded to include professional occupations or livelihoods within which a particular viewpoint or presumption or interpretive inclination predominates.
I undertook arduous, minute-long searches in the Ngram viewer (nothing) and on the google for search strings
"that's a cold pizza"
"it's a cold pizza"
"he's a cold pizza"
"was a cold pizza"
"is a cold pizza"
I got lots of restaurant reviews (mostly negative, of course), a link to the lyrics of the song "Cold Pizza Warm Beer" by Gaye Adegbalola
It’s just the morning after, I don’t remember who was here.
I’ll eat a slice of that cold pizza, and wash it down with warm beer.
references to the sports talk show on ESPN2, and instructions for making a palatable breakfast. Possibly the song lyric is metaphorical. I was about to give up when I ran into this from an article in Time Magazine (August 29, 2011) entitled "Another Slice of 'Cold Pizza'? The Man Most Likely to Lead Japan" about then Japanese Finance Minister Yoshihiko Noda, who was expected to become Prime Minister:
Can Noda lead? Analysts are not sanguine. "He emerged as a
compromise," says Jeff Kingston, Director of Asian studies at Temple
University Japan. "He's not charismatic, or a populist or a good
communicator, [and] not a particularly bold or visionary leader. He's
sort of a 'Steady Eddy' and doesn't raise expectations that much. ... Says Yoshi Yamamoto, a political advisor to DPJ [Democratic Party of Japan] congressmen: "Noda seems a bit like the former LDP [Liberal Democratic Party] prime minister Keizo Obuchi [in the 1990s], generally known internationally as a 'cold pizza,' but respected domestically by working level staffers and officials as someone who listens and rewards."
I can find no uses for Urban Dictionary's claims for sexual and drug connotations.
Best Answer
In U.S. sports, the tradition of naming all-star teams—either to play each other in one-off contests or to recognize the best players of the year—is an old tradition. We find examples going back to "Begin Doping Out All-Star Elevens," in the [Phoenix] Arizona Republican (December 4, 1910):
Fans of U.S. football will note that the four players thus designated in 1910 by all four sources that the sportswriter consulted (and thus consensus picks) were guys from Brown, Harvard, Penn, and Yale—four Ivy League schools. In fact, aside from one player from Navy and one from Army, every player designated as an All-American by the four sources cited was from an Ivy League school.
Instances of "dream team" begin to reappear in the Great War era, several of them in connection with a football game played in El Paso in 1916 between two military units with star players from various college teams. From "Football Oder of Today's Sport Card," in the El Paso [Texas] Morning News (November 5, 1916):
From "Vansurdam's Football Column," in the El Paso [Texas] Morning News (December 13, 1916):
And from "Army Baseball Fan Chooses All-Star Dream Team From Military Leaguers; Interesting Problem at Second Base," in the El Paso [Texas] Morning News (April 25, 1918):
The phrase "dream team" undoubtedly arose from two considerations: it rhymes (an irresistible lure to sports writers then and now); and the team thus imagined had no chance (under normal circumstances) of playing together as a team in reality—at least not in the 1910–1918 era.
The Encyclopaedia Britannica article that Josh61 sites in his question actually refers to the U.S. Military Academy's team at West Point near the end of World War II:
This was the 1945 Army team that starred Doc Blanchard and Glenn Davis. Although misdated as being published in 1929 in Google Books search results, the quoted text was actually written after the World War II, though probably not later than 1954.
In this case, "dream team" meant "ideal but actual"—as it did when applied to the U.S. national basketball team in the 1992 Olympics—not (as in most earlier instances) "ideal but imaginary."