"How would you like it cooked?" suggests you are asking someone HOW they want their food cooked, for example, "How would you like your eggs cooked? Boiled? Fried?"

"How cooked would you like it?" suggests you are asking someone HOW MUCH they want you to cook their food, for example, "How cooked do you want your broccoli? Do you want it hard or soft?"

I hope this helps!