A mulligan is a stew, often made with various leftovers. You might clean all the vegetables out of your fridge and whip up a mulligan.
When you make a mulligan — also called a mulligan stew — you use odds and ends from your refrigerator and pantry. You can also use the word to refer to a specific situation in the game of golf: if you make a terrible shot, a mulligan is when you're allowed to try again. The stew came first, around 1905, and the golf stroke followed in the 1940s, possibly from the name of a specific Canadian golfer.