Arrange 6 noodles in a 9×13-inch baking dish, breaking if necessary to fit. Spoon 1/2 of the sauce over noodles. Top with 1/2 of the cottage cheese and 1/2 of the mozzarella cheese. Repeat layers with remaining noodles, sauce, cottage cheese, and mozzarella cheese. Top with Parmesan cheese. Cover tightly with foil; refrigerate overnight.