Learn English – Does “What did you get up to?” make sense

A number of the earliest instances of "but I digress" that a Google Books search for that phrase finds appear as part of longer expressions.

The most common of these longer clauses is the phrase "But I digress too far"—an expression that appears in Richard Baxter, Poetical Fragments: Heart-Imployment with God and It Self (1689) [the last sentence in a paragraph]; in Browne Willis, Notitia Parliamentaria, or An History of the Counties (1715) [the first clause of the first sentence of a new paragraph]; and in John Ray, The Wisdom of God Manifested in the Works of the Creation (1717) [the last sentence in a paragraph].

Likewise, the phrase "But I digress too much" appears at the beginning of a sentence and line of verse in John Chalkhill & Izaak Walton, Thealma and Clearchus: A Pastoral Romance (1683).

And the phrase "But I digress from my Design" appears at the beginning of a sentence and line of poetry in Samuel Butler, "The Whig's Ghost", in Posthumous Works in Prose and Verse (1717).

In all of these instances, the phrase containing "but I digress" occurs in the context of an author who has caught himself going off on a tangent from the main point of the discussion. The observation comes after the fact of having digressed already and of continuing (at least until the moment of making the observation) to digress.

The earliest of the ten unique matches for "but I digress" that a Google Books search finds for the period 1600–1718 uses the phrase similarly to the way the longer expressions do—as an after-the-fact observation. To convey a sense of how the phrase works in place, here is the final third of the relevant paragraph from The Religion of Protestants: A Safe way to Salvation (1674):

As therefore the light, determining the Eye to see, though it presupposeth the Eye which it determines, as every Action doth the object on which it is imployed, yet it self is presuppos'd and antecedent to the act of seeing, as the cause is alwaies to its effect: So, if you will suppose that Scripture, like light moves the Understanding to assent, the Understanding (that is the eye and object on which it workes) must be before this influence upon it; But the Assent, that is, the belief where to the Scripture moves and the Understanding is moved, which answers to the act of seeing, must come after. For if it did assent already, To what purpose should the Scripture do that which was done before? Nay, indeed, How were it possible it should be so; any more than a Father can beget a Son that he hath already? Or an Architect build a house that is built already? Or that this very world can be made again before it is unmade? Transubstantiation indeed is fruitful of such Monsters. But they that have not sworn themselves to the defence of Error, will easily perceive, that jam factum facere, and factum infectum facere, are equally impossible. But I digress.

In the preceding excerpt, everything from the sentence beginning "Nay, indeed, How were it possible ..." amounts to a digression from the earlier line of argument comparing Faith to the human eye and Scripture to light.

This is typical of the context in which "but I digress" appears in the ten earliest Google Books instances; and I believe that the phrase remains true to its origins in being applied today, in the vast majority of instances, backward as a comment upon a digression already committed, rather than prospectively upon a digression about to occur.

If you replace way by thing, then your sentence is grammatical and makes sense:

Pretending to be a beggar on the street was the only thing such a shameless individual as you could do.

This works because you can do things but you cannot do ways. For example,

• Begging was the only thing (that) she could do.

• ?Begging was the only way (that) she could do.

However, you can have ways. So your friend's suggestion:

Pretending to be a beggar on the street was the only way such a shameless individual as you had

is grammatical and makes sense