Cook spaghetti in a Dutch oven according to package directions, omitting salt and fat. Add carrot to spaghetti during last 2 minutes of cooking time. Drain. Place pasta mixture in an 11- x 7-inch baking dish coated with cooking spray; stir in pasta sauce. Set aside.
Combine ricotta cheese, egg, and 1/2 teaspoon salt in a small bowl; stir until smooth. Spread ricotta mixture over pasta mixture.
Heat olive oil in Dutch oven over medium-high heat until hot; add garlic, spinach, and remaining 1/4 teaspoon salt. Cover and cook 2 minutes or until spinach begins to wilt; cook, uncovered, stirring constantly, 3 minutes or until liquid evaporates. Arrange spinach over ricotta mixture. Sprinkle mozzarella cheese over top of spinach.
Cover and bake at 350° for 20 minutes. Uncover and bake an additional 5 minutes or until thoroughly heated and mozzarella cheese melts.