Real Dictionary

cook up
phrasal verb: If someone cooks up a dishonest scheme, they plan it.
phrasal verb: If someone cooks up an explanation or a story, they make it up.
phrasal verb: If you cook up a quantity of food, especially a large quantity, you heat it until it is ready to be eaten.

cook up in American English
to concoct or contrive, often dishonestly
to concoct; devise; invent

cook up in British English
to concoct or invent (a story, alibi, etc)
noun: (in the Caribbean) a dish consisting of mixed meats, rice, shrimps, and sometimes vegetables