"TK seems to be in dire need of a brain to munch on."
Get TK some brains to eat.
The objective is to kill zombies with head shots, collect ten of the brains that fall, and return them to Zombie TK Baha.
"You gave him a few brains. He appears to be coughing up an item..."
"Brains" is all T.K. can talk about.
Any brains picked up without this mission or the ones following do not count and are unusable.
As long as a player stays in a zone, the brains that drop from zombies will remain on the ground until picked up. Therefore, if a player has completed the mission, with characters in Hallow's End, the extra brains can be left on the ground for the next Brains mission.
After the mission is turned in, TK will eat a brain and vomit up an item. It will be a shock artifact if not already received; otherwise, he drops a random item.
When T.K. is talking about all the different ways to cook brains, this is from the movie 'Forrest Gump' in which the title character's friend lists all the ways to prepare shrimp that he can think of. See: Benjamin Buford 'Bubba' Blue of Forrest Gump
T.K.'s quote about brains, that you can "Boil 'em, mash 'em, stick 'em in a stew..." is a reference to The Lord of the Rings: The Two Towers in which Samwise Gamgee explains to Gollum what "taters" are.
Despite the background, T.K. does not need to be dead to begin this.