Green’s Dictionary of Slang

cheese n.3

[cheese v.3 ]

a smile.

[UK]N&Q CLVIII 119/1: Another slang use of the word ‘cheese’ was in vogue at Rugby School... This was with the meaning ‘smile’, both verb and noun.
[UK]F. Norman Guntz 101: If some one is a thorough shnide [...] you must still give him the big cheese whenever you see him.

In phrases