'egg-producing' originates from Modern English, a compound of the noun 'egg' and the present participle 'producing' (from the verb 'produce'), where 'egg' meant 'an egg' and 'produce' meant 'to make or bring forth'.

'egg' comes from Old English 'æġ'. 'Produce' comes from Latin 'producere' (pro- 'forward' + ducere 'to lead'), passed into Old French (e.g. 'produire') and Middle English as 'produce'/'producing', and the modern compound 'egg-producing' was formed in Modern English by joining 'egg' + 'producing'.

Initially, 'egg' simply referred to the biological egg and 'produce' originally carried the sense 'lead/give forth'; over time 'produce' developed the narrower sense 'make or bring into existence', so the compound now specifically means 'making or laying eggs'.