1.
If someone cooks up a dishonest scheme, they plan it. (INFORMAL)
He must have cooked up his scheme on the spur of the moment.
PHRASAL VERB: V P n (not pron), also V n P
2.
If someone cooks up an explanation or a story, they make it up. (INFORMAL)
She’ll ~ a convincing explanation.
PHRASAL VERB: V P n (not pron), also V n P