AWAD on 11/13 discussing the word, "mulligan" stated:

"Both senses of the word are from the name Mulligan. It's not certain who these two Mulligans were -- maybe a golf player and a chef. Earliest documented use: 1936. "

OED has the stew reference from 1899.

I always assumed, but never bothered to look it up, that this came from "mulligitawny."

Translated literally from Tamil, "Mulligatawny" or "Milagu thanni" means "pepper water" ("Millagu" means pepper and "thanni" means water).