I would drop any reflavouring in favour of making it fun to be a cook outside of combat.
What does his character want to achieve? And what are his ideals? Then try to give him objectives to work towards.
For example: his goal might be to find a fabled ingredient. You can then drop hints on where to find it. Or he might want to be the most renowned chef in the world, after which you insert a cooking competition that requires special ingredients (that just so happens to be found in the same dungeon the party was supposed to head to anyway).
As for examples on ideals: Feed anyone that is hungry (without harming them via the food). Try to cook/eat anything (causing them to want to hunt/gsther stuff. Never use your hands to fight, to keep them clean for cooking (might need some reflavouring of abilities).
These examples make, that his cooking gives his character a reason to do things, rather then just be the thing he does.
Neither of you will remember how many dice were used to slay that monster. But the memory of how his character sliced up the monster for ingredients, only for some treasure or quest item to pop out of the belly, will certainly remain.
Not just art. They were making memes. Every strip has the same structure: Everett makes a statement of common decency, some random dude disagrees, then Everett physically assault the random dude. This is literally a meme template, from the early 1900s.
Question is: will the meme evolve in a similar fashion that we see modern memes evolve? Or does the fact that it has a single author prevent this natural evolution?