Learn Russian: Благодаря трёмстам граммам белка это блюдо очень полезное. - Thanks to three hundred grams of protein, this dish is very healthy.

When declining hundreds in Russian, you have to change both halves of the word. The first half declines like the number 3 in Dative (трём), and the second half declines like the Dative plural of 100 (стам). Mash them together, and you get трёмстам.

Normally big numbers force the following noun into the Genitive plural. Why is it трёмстам граммам (Dative plural) instead of граммов?

The rule where numbers force a noun into the Genitive only applies when the number is in the Nominative or (inanimate) Accusative case. In all other cases—like the Dative here—the number simply matches the case of the noun. Because the sentence requires the Dative case, both the number and the noun take Dative plural endings.

Doesn't белка mean "squirrel"? Why is there a squirrel in this dish?

It looks exactly like the word for squirrel, but here белка is actually the Genitive singular form of белок (protein). Белок has a "fleeting vowel"—the о drops out when you add case endings. So "of protein" becomes белка. (Funnily enough, the word for squirrel is белка, and its Genitive plural is белок, so their forms are complete mirror images of each other!)