Preheat oven to 350. Cook noodles according to package directions for 20 minutes. Blend soup and milk till smooth. Add onions and mushrooms to soup mixture. Drain noodles. Layer 1 1/2 cup noodles, 1/2 cup tuna and 1 cup broccoli in each of two casserole dishes. Pour 1 cup sauce over each.Repeat, ending with sauce. Bake for 20 minutes. Add 1 cup cheese to top of casseroles. Bake 15 minutes longer and serve.