Preheat oven to 350 degrees F. Lightly coat a 2-quart rectangular baking dish with cooking spray.
In a medium bowl stir together egg, ricotta cheese, spinach, garlic, and pepper. In a separate bowl combine Alfredo sauce and milk.
Spread about 1/2 cup of the Alfredo sauce mixture into the bottom of the prepared baking dish. Arrange three of the uncooked noodles in a layer over the sauce. Spread half of the spinach mixture over the noodles; top with half of the carrots and half of the mushrooms. Arrange the remaining three uncooked noodles over the vegetables. Top noodles with the remaining spinach mixture. Top with the remaining carrots and the remaining mushrooms. Cover with the remaining Alfredo mixture. Sprinkle with the mozzarella cheese and Parmesan cheese.
Lightly coat a sheet of foil with cooking spray. Cover dish with foil, coated side down.
Bake for 60 to 70 minutes. Uncover. Bake for 15 to 20 minutes more or until top is lightly browned. Let stand for 20 minutes before serving.