Green’s Dictionary of Slang

cheese n.³

a smile.

1930		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.
1962		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

chuck a cheesy (v.)

(Aus.) to grin.

1992

K. Lette Llama Parlour 93: I chucked a huge cheesy in their direction.