Preheat the oven to 325 degrees F (165 degrees C). Press one package crescent roll dough into a 9-inch baking dish; cut remaining package crescent roll dough into 1-inch strips.

Stir eggs, ham, Cheddar cheese, and Parmesan cheese together in a bowl; pour mixture into prepared baking dish. Arrange crescent roll strips over ham mixture creating a crisscross pattern.

Bake in preheated oven until golden brown and set, 50 to 60 minutes.