Collocations for cheese - noun

hard, soft
sharp, strong
mild
fat-free (AmE), full-fat, low-fat, reduced-fat
grated, shredded (AmE)
grilled, melted
processed, string
blue, cottage, cream, curd (esp. BrE), goat's, smoked
Cheddar, Parmesan, etc.
specialty (AmE)
Dutch, Swiss, etc.

chunk, hunk, lump (esp. BrE), piece, slice

make
cut, grate, slice
Cut the cheese into cubes.

melt
sprinkle (sth with), top (sth with)
Sprinkle the cheese over the beans.
Sprinkle the potatoes with grated cheese and grill for a few minutes.

fondue, omelette, roll, sandwich, sauce, soufflé
stick (esp. AmE)
board (usually cheeseboard)
plate, platter (both esp. AmE)
grater
factory

bread and cheese
cheese and biscuits (BrE), cheese and crackers
cheese on toast (BrE)
a selection of cheeses