익히다 is the causative of 익다 — you cook the food rather than the food cooking itself. -게 says to what point: 완벽하게 익혔는가 (whether it's cooked all the way through), 어떻게 스테이크를 이렇게 부드럽게 익혔을까? (how did they cook the steak so tender), 먹기 좋게 익혀서. The same verb also means learning something until it becomes second nature, which is what 한번 쉽게 익혀봅시다 is.