E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
Cheese.
Something choice (Anglo-Saxon, ceos-an, to choose; German, kiescn; French, choisir). Chaucer says, To cheese whether she wold him marry or no.
1
Now thou might cheese
How thou couetist [covetest] to calme, now thou
Knowist all mi names.
P. Ploughmans Vision.
It is not the cheese. Not the right thing; not what I should choose.
2
He is quite the cheese or just the cheesei.e. quite the thing. By a double refinement we get the slang varieties, Thats prime Stilton, or double Glosteri.e. slap bang up.