Even if you're greedy, you won't be able to eat it all.

Literal

Be-greedy-[even-ても] eat-finish-can-not [emphasis-よ].

欲張る ('to be greedy / act greedy') is a verb from 欲 ('want') + 張る ('stretch'). 食べきれない uses the compound verb 食べきる ('eat completely') in potential negative — 'can't eat all of it.' ~きる is a productive auxiliary meaning 'complete X fully.'