Preheat an oven to 350 degrees F (175 degrees C). Spray a 9x13 inch baking dish with cooking spray.
Pour the beaten eggs into the prepared baking dish. Bake in the preheated oven until they set and are no longer runny, 8 to 10 minutes. Remove, allow to cool, and cut into 6 portions.
Butter the cut sides of the croissants and place one portion of the cooked egg onto each croissant bottom. Top each sandwich with two slices of ham and a slice of Colby-Jack cheese. Place the croissant tops on top of the sandwiches; wrap each sandwich well with plastic wrap. Place the sandwiches onto a baking sheet; freeze until solid, about 3 hours. Store frozen.
To reheat, cook a wrapped sandwich in a microwave on High until hot in the center, 1 to 2 minutes.