"To break eggs" or "to crack eggs"?

? She cracked an egg into the frying pan.

In this sentence, should cracked be replaced with broke?
I take that to crack means to break, but without causing a complete separation of the parts.

The windshield of this car was cracked.

Both verbs are quite commonly used with eggs. Comparing various phrases in the Google n-grams viewer (“cracked/broke an egg”, “crack/break the eggs”, etc.) gives the impression that in the late 19th century break became more common, but that recently crack has been making a bit of a comeback.

The relative frequencies vary quite a bit between phrasings (eg in “breaking/cracking eggs”, breaking dominates by a large margin, presumably due to “You can’t make an omelette without…” and similar phrases). However, the same historical trends seem to hold for all the phrasings I tried.

As @nohat points out, crack can be used with this meaning in other contexts as well, though it seems to be less common in general than it is with eggs.

You're right about the meanings of the words. But both verbs are used with egg. See the examples:

Never crack eggs directly into the bowl that you are building your recipe in.

Cracking an egg open and separating the egg yolks is quite easy.

Make sure they're not wearing any rings and challenge them to break an egg this way.

Breaking an egg with one hand takes finesse, but using two hands to crack eggs works just fine.

The verb crack can mean “to break by creating cracks”, or as Merriam-Webster Dictionary says “1a: to break so that fissures appear on the surface <crack a mirror>”