In a large skillet, in heat oil over medium heat. Add onion, carrot and garlic. Cook for 5 minutes or until just tender, stirring occasionally. Add beans, undrained tomatoes, the ¼ cup parsley, the 1 tablespoon basil, and the 2 teaspoons oregano. Bring to boiling; reduce heat. Simmer, covered, for 15 minutes.
Meanwhile, cook lasagna noodles according to package directions; drain and rinse with cold water. Drain again.
Preheat oven to 375°F. With a potato masher, mash beans slightly in skillet. Add mushrooms to skillet; simmer, uncovered, for 15 minutes more, stirring occasionally. Meanwhile, in a medium bowl, combine cottage cheese, ½ cup of the mozzarella cheese, the egg and Parmesan cheese; set aside.
Spread ½ cup of the bean mixture in a 2-quart rectangular baking dish. Arrange two noodles in a single layer on top of the bean mixture. Spread with one-third of the cheese mixture. Top evenly with one-third of the remaining bean mixture. Top with half of the spinach. Repeat layers twice, starting with noodles and ending with bean mixture.
Bake, covered, for 40 minutes or until heated through. Top with remaining mozzarella cheese. Bake, uncovered, 5 minutes more or until cheese is melted. Let stand for 10 minutes before serving. If desired, top with the 2 tablespoons fresh parsley, basil and/or oregano.