In 2-quart saucepan over high heat, heat crushed tomatoes, garlic, basil, salt and pepper. Over high heat, heat to boiling; reduce heat to low. Simmer uncovered, 10 minutes to blend flavors.
Preheat oven to 375 degrees F. Grease 12" by 8" baking dish. In medium bowl combine ricotta cheese and egg until well mixed. Spoon some tomato sauce on bottom of dish to coat. Place 3 noodles lengthwise across the pan. Top with 1/3 of tomato sauce. With a spatula, spread 1/3 of ricotta mixture. Scatter 1/3 of carrots and spinach on ricotta and 1/3 of mozzarella cheese. Repeat with noodles, tomato sauce, ricotta, vegetables and mozzarella two more times. Sprinkle with Parmesan cheese.
Cover dish with foil; bake 30 minutes. Uncover dish; bake 10 minutes longer. Let stand 15 minutes before cutting.
