Heat soup with broccoli until broccoli is thawed. Cook carrots and onions
in 1 Tbsp oil until lightly browned. Reduce heat to low. Add 1/4 cup water
and cover. Simmer until cooked, about 15 minutes. Remove to a bowl. In 3
Tbsp oil, cook mushrooms until moisture is gone. Stir in carrot mixture.
Mix cheeses and eggs. Set oven to 375F.
Place 1 cup sauce in pan. Layer with 1/2 of noodles, 1/2 of cheese
mixture, all of carrot mixture, 1/2 remaining sauce, remaining noodles,
cheese and sauce. Cook for 45 minutes.