In a large skillet, cook beef over medium heat until no longer pink; drain. For barbecue sauce, in a large saucepan, combine the next 13 ingredients. Bring to a boil. Reduce heat; simmer, uncovered, for 10 minutes.
Spread about 1/4 cup barbecue sauce in a greased 13-in. x 9-in. baking dish. Layer with three noodles and half of the beef. Spread with half of the remaining barbecue sauce; sprinkle with half of the mozzarella, cheddar and Colby cheeses. Repeat layers.
Combine cottage cheese and egg; spoon evenly over the top. Bake, uncovered, at 350° for 50-60 minutes or until lightly browned. Let stand for about 10 minutes before cutting.