Do not let players use some homebrew they find online. It's almost always overpowered garbage.

I'd recommend that you talk to the player about what exactly is the fantasy they are looking for.

The D&D classes are primarily packages of mechanics for what a character does inside of combat. One does not cook during combat. Realistically, being a cook is more about how you roleplay outside of combat. They can pick whatever class they want, as long as they support the cook fantasy with their other choices.

You could maybe work with the player to come up with a custom background and have them use the "Chef" feat from Tasha's Cauldron of Everything as the background bonus, which is only mechanical support you will find for being a cook in 5e.

If your player wants to be Senshi from Delicious in Dungeon, they are going to have a bad time. There are simply no mechanics to support that much cooking. Nutrition isn't modelled in D&D, there isn't a monster harvesting system, every table I've ever played at forgets to even mark off rations during rests. You could homebrew a whole new mechanic for food, but this would be a big effort and may be hard to balance in a way that's fun for everyone at the table.

Don't be afraid to tell the player "no" if you don't think D&D is the right game to achieve the fantasy they want. It's better to rip that Band-Aid off quickly rather than have the game system do it over several sessions.

Assuming this is 5e you have a few different options:

• Background: Guild Artisan (PHB), taking the proficiency in cook's utensils and using the extra rules such as Prepare Meals from XGE
• Feat: Chef (TCE), a different way to get the cook's utensils proficiency and it comes with some nice healing bonuses, make your race variant human (PHB) or custom lineage (TCE) to get this at level 1
• Class: Artificer (Alchemist) (TCE) - the artificer is all about re-flavouring spells as different things, potions can easily become magically-prepared food and drink

All simple options from "core" books, eat your fill!

I'd say to treat it like a profession and not a class. Like you would a Blacksmith or Barmaid.

Maybe there are some custom profession stuff available somewhere you can build off, but yeah, most of it would be flavor (pun intended).

Embrace the flavor. And by flavor, I mean change the theme of your character without changing the mechanics.

Is that a dagger or an incredibly sharp sushi knife? Is that a longsword or a butcher's cleaver?

I personally have made this character as an artificer but you could do it as a rogue. A highly skilled chef who knows exactly how to cut (sneak attack). As an adventurer, you seek out new flavors and styles of cooking and aren't affraid to try some dragon steaks, with harpy eggs, with a side of black ooze gelato.

Also there is a single feat that really helps push it.

Re flavoring spells seems like the easy way to go about this:
Acid arrow: marinate & tenderize!
Any fire spell: flambe!
Viscous mockery: IT'S RAW!
Mage hand: sous chef.

Or, think about it differently, like Sanji from one piece, where cooking is his thing, but he's also a solid fighter. (That will not use knives or his hands to fight, those are for cooking)

As said by others, rather reskin existing mechanics, than use homebrew

The most suited for something akin to coocking in combat would probably be a cleric where you can use existing buff spells or effects and just change how they do it rather than what they do

Cure wounds is just an "emergency sandwich"

Bane is making "thousand year egg" so very smelly, that it distracts the enemy

I would recommend also to use new names for these abilities so that they have it easier to stay in character and ask them how they think a specific effect that their class has can be produced with food

I would also say for the purpose of a fight that most dishes are pre prepared (I.e. representing the spell slots they have) and are than just used in combat

Mhm 5e and other derivates have a Cook Background. So why not use it?

Sure it's more leaning into the roleplaying aspect but would you really think it's believable that someone is attacking or defending someone with perfectly fried chicken?

A martial arts cook is a force to be recon with as many Action Movies featuring Steven Segal have shown us.

Ah the culinary artificer. It all started with banging rocks and sticks together. That's how I discovered cinnamon and my life changed.

I'd suggest this http://dnd5e.wikidot.com/artificer:alchemist

And just give them double proficiency or advantage on anything to do with food.

Come up with a list of reasonable buffs (e.g., +1 ac until next rest) in exchange for spending time cooking during a long rest doing cooking instead of keeping watch.

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.