'broad-billed' is a modern English compound formed from 'broad' + 'billed', where 'broad' meant 'wide' and 'billed' is the past-participle/adjectival form of 'bill' (beak).

'broad' originates from Old English 'brād' meaning 'wide', and 'bill' (meaning 'beak') comes from Middle English 'bil'/'bile' (from Old Norse/Germanic sources); the compound form 'broad-bill' and adjectival 'broad-billed' developed in Modern English by combining these elements.

Initially the separate words meant 'wide' and 'beak'; when combined as 'broad-billed' the meaning became the descriptive adjective 'having a wide beak', which remains the current meaning.