cook up vs hatch

cook up is not a noun while hatch is a noun.

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

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

Other hypernyms of cook up include concoct, dream up, think of, think up.

cook up (noun)	hatch (noun)
	a movable barrier covering a hatchway
	a sloping rear car door that is lifted to open
	shading consisting of multiple crossing lines
	the production of young from an egg

cook up (verb)	hatch (verb)
concoct something artificial or untrue	sit on (eggs)
prepare or cook by mixing ingredients	emerge from the eggs
	draw, cut, or engrave lines, usually parallel, on metal, wood, or paper
	devise or invent
	inlay with narrow strips or lines of a different substance such as gold or silver, for the purpose of decorating