I agree with you. One can cook up some potatoes to eat.
Student or Learner
I would appreciate if someone could explain this to me.
You can cook a potato.
Can you cook up a potato?
To me cooking up a potato seems like a creation of some sort as up suggest here.
'Cooking' is a blanket term for a series of steps used to create a dish of food- often involving the use of heat in some way. Of course, one can 'cook up' some food.
For specific food items, we usually have more specific terms for the way we prepare them. One doesn't usually 'cook' a potato. One boils, bakes, fries or uses some other method to prepare a potato for eating.
For me, the phrase 'cook up' is mostly used as a metaphor for creating some excuse or reason to do something not related to food.
"Where is Tom today?" "Oh, he cooked up some excuse about having to take his kid to the dentist. That kid goes to the dentist about as often as I go to the bathroom!"