It can be omitted before all three, in the right context.
If you're simply talking about things you're good at cooking, don't use the article.
If you're talking about a specific plan to cook a specific meal, the article might be used.
Also note that "make" is more common than "cook" in everyday conversation in BrE.
Helen: Are you a good cook?
Sam: I'm not bad! I can make a delicious split pea soup and a great tagliatelle in creamy mushroom sauce.
Robbie: Mum, what's for dinner?
Mum: I'm not sure yet. I can make pizza or pasta. Which would you prefer?