vamp vs cook up

vamp is a noun but cook up is not a noun.

Word	Noun	Adjective	Verb	Adverb
vamp	Yes	No	Yes	No
cook up	No	No	Yes	No

As verbs, cook up is a hypernym of vamp; that is, cook up is a word with a broader meaning than vamp:

Other hypernyms of vamp include fabricate, invent, make up, manufacture.

vamp (noun)	cook up (noun)
piece of leather forming the front part of the upper of a shoe
an improvised musical accompaniment
a seductive woman who uses her sex appeal to exploit men

vamp (verb)	cook up (verb)
provide (a shoe) with a new vamp	concoct something artificial or untrue
act seductively with (someone)	prepare or cook by mixing ingredients
piece (something old) with a new part
make up