After getting some feedback from some of my fellow artists I mixed and matched different parts from my 5 Cook concept sketches. The result is shown below. I tried to also match the style used by Valve to showcase their character concepts.
Out of all the different ideas I came up with for a hypothetical new character for Team Fortress 2 I decided to go with "The Cook". Here are a few sketches I made with different options for the look of The Cook.