Preheat oven to 350 degrees F. Coat a shallow 2-quart baking dish with cooking spray.
Press spinach in a mesh strainer to get out as much moisture as possible. Pulse in a food processor until very finely chopped.
Combine milk, flour, salt, pepper and nutmeg in a large saucepan. Cook over medium heat, whisking, until thickened, 2 to 4 minutes. Remove from the heat and stir in 1/2 cup Cheddar, cottage cheese and the spinach.
Beat egg whites in a large bowl with an electric mixer, slowly increasing the speed, until they begin to foam. Continue to beat until the whites hold their shape; do not overbeat. (You'll know they are ready when you lift the beaters out and the peak doesn't flop over.)
Gently fold the whites into the spinach mixture with a rubber spatula until uniform. (It's OK if a few white streaks remain.) Transfer to the prepared baking dish.
Bake for 35 minutes. Top with the remaining 1/2 cup Cheddar; continue baking until the cheese is melted, about 10 minutes more. Let stand for 5 minutes
To make ahead: Prepare Steps 2 & 3, refrigerate for up to 1 day. Bring to room temperature before folding in egg whites.
1 vegetable, 1/2 high-fat protein, 1/2 lean protein