eat one's fill

eat one's fill AND fill up (on sth) (eat until one is satisfied, eat as much as one can) — есть досыта, наедаться; ~ есть досыта, до отвала; есть, пока лезет

Example 1: Eat your fill. You won't have another meal till tomorrow.

Example 2: If you’re hungry, fill up on pasta or rice. (MM)

fill sb up (with sth) — кормить досыта, накормить досыта

Example: They filled me up with cakes and sandwiches. (MM)

cf.
have had one's fill (to have had enough to eat or drink)

Related vocabulary:
[объесться]
[have a hollow leg]
stoke up
(to eat a lot of food, for example because you will not eat again for a long time; to fill oneself with food) хорошо поесть (впрок), хорошенько заправиться (едой); наедаться досыта впрок
..... Stoke up! You won't be eating again for a while!

stoke up on/with sth (to eat a lot of a particular food in order to avoid feeling hungry or weak late)
..... We stoked up on hot soup before going out in the snow. (LDOCE)
..... As it was a cold morning, she stoked up on bacon, eggs, and beans on toast. (CALD)
..... Stoke up for the day on a good breakfast. (OALD)