Lightly butter 13 x 9 x 2-inch oven-proof dish. Cook egg noodles slightly less than al dente; drain. Layer half of noodles, covering bottom of dish. Top noodles with half of vegetables. Cover with 1 cup each fontina, provolone and havarti cheese and 3/4 cup sauce. Top with remaining noodles, vegetables and sauce. Cover with remaining cheese.
Bake 20 minutes covered. Uncover and baked 20 more minutes until bubbly and golden.