Learn English – the origin of the phrase “a penny for your thoughts”

an early occurrence is from Olympic Games by Isaac Cruikshank:

3. In settle (someone’s) hash, to subdue, silence, defeat; kill: s. >, in C.20, coll. An early occurrence is in Isaac Cruikshank, Olympic Games, 16 June 1803 (thanks to Mrs M.D.George).

it's also in Americanisms: The English of the New World (1872) by M. (Maximilian) Schele de Vere - here's an image:

from hash:

1657, "to hack, chop," from Fr. hacher, from O.Fr. hache "axe." The noun "stew" is first recorded 1662, from the verb.

My educated guess is that it's related to the the origins of the phrase "bury the hatchet", relevant quotes being:

"Bury the hatchet" is an Indianism (a phrase borrowed from Native American speech). The term comes from an Iroquois ceremony in which war axes or other weapons were literally buried in the ground as a symbol of newly made peace. The other two languages spoken by Europeans in close contact with the Iroquois in and around what is now New York state also use the phrase: enterrer la hache de guerre and de strijdbijl begraven. (I leave it as an exercise for the reader to determine which is French and which is Dutch.)

and

The first mention of the practice in English is to an actual hatchet-burying ceremony. Years before he gained notoriety for presiding over the Salem witch trials, Samuel Sewall wrote in 1680, "I writt to you in one [letter] of the Mischief the Mohawks did; which occasioned Major Pynchon's goeing to Albany, where meeting with the Sachem the[y] came to an agreemt and buried two Axes in the Ground; one for English another for themselves; which ceremony to them is more significant & binding than all Articles of Peace[,] the hatchet being a principal weapon with them."

So between MikeVaughan's answer that it's related to the French word for "axe" & the practice of "burying the hatchets", I'm inferring that "settle someone's hash" came from these ideas.

It’s true that this expression is in an interrogative form that is not normally found in contemporary English. It uses inversion rather than the auxiliary verb do. We would normally expect What do you have? (or, in the UK at least, What have you got?) It’s a colloquial way of saying, in the Oxford English Dictionary’s definition, ‘anything else (similar) that there may be, or that one can think of’, or even, simply, etcetera. It’s of US origin, and the Oxford English Dictionary’s earliest citation is from the 'New Yorker' magazine in 1925.