What would you do if you were invisible?

I would probably sneak into the backyard of my favorite restaurant and research their recipe.

I would use "sneak into the..." as it has the feeling of infiltration. Like a ninja.
"Backyard" gets the point across but I think just "back" or "back alley" of the restaurant sounds more natural. Backyard has more of a "lawn, swimming pool, behind-the-house" feel to it.

Ratatouille, particularly, is my favorite food in particulardish at theat restaurant but I can't cook like thatey can.

I would use "dish" over "food" when you're talking about a single prepared menu item.
And this sentence structure has a more natural flow in my opinion.

What do you want towould you do?

You're restating the original question, "What would you do (if you were in visible)?"

I would probably sneak into the backyard of my favorite restaurant and research their recipe.

Backyard, an object, needs an article.

Recipe, another object, also needs an article. You can just use "the" again, but I used "their," which is better because it's more clear.

If you want words in place of 'research', you could say "steal," "copy," "memorise,"

Ratatouille, in particular, is my favorite food in particular at theat that restaurant, but I can't cook like thatem.

Because you've already introduced the restaurant, it makes more sense to say THAT restaurant, instead of just the restaurant.

I can't cook like that is okay, but them is better because it's clearer.

What would you do if you were invisible?

I would probably sneak out to the backyard of my favorite restaurant and research a recipe.

Ratatouille is my favorite food indish, particularly at theis restaurant but I can't it cook like that.

What wouldo you want to do?

What would you do if you were invisible?

I would probably sneak to the backyard of my favorite restaurant and research their recipes.

Ratatouille is my favorite food in particular at the restaurant, but I can't cook like thate restaurants can.

What wouldo you want to do?