"TK's hunger seems to be growing. Find him more brains."
Head back to the town of Hallow's End and go on a zombie killing rampage. Aim for the head, only headshots will cause zombies to drop their brain.
You may want to head off on some other missions while you collect brains.
" You gave him a bunch of brains. He appears to be coughing up an item..."
After turning in the mission wait for TK to eat a brain and he will vomit up an item, such as a weapon, COM or Artifact.
Keep in mind that as long as you stay in a zone the brains that drop from zombies will remain on the ground until you pick them up. Therefore, if you have completed the mission leave the extra brains on the ground so you can collect them when you get the next mission.