Green’s Dictionary of Slang

1. superlative, best, optimum.

1970		F. Collymore Notes for Gloss. of Barbadian Dial. 29: A cheese boy was a dude, a cheese girl, one’s sweetheart.
1982–2004		G. Sculatti Catalog of Cool 🌐 cheese (adj.): Top of the line in its class. The 1958 Eldorado is unquestionably ‘the cheese Caddy.’.

2. see cheesy adj.² (1)