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.