'thinly-cut' is a compound word formed from 'thinly' (meaning 'in a thin manner') and 'cut' (meaning 'to divide with a sharp instrument').

'thinly' comes from Old English 'þynne' (thin) + '-ly', and 'cut' comes from Middle English 'cutten'. The compound 'thinly-cut' emerged in modern English to describe something sliced thinly.

Initially, it simply described the manner of cutting, and it still retains this meaning today.