1. Preheat oven to 400°.
2. Heat oil in a large nonstick skillet over medium-high heat. Add zucchini, onion, and carrot; sauté 8 minutes or until lightly browned. Remove from heat; stir in corn, basil, 1/4 teaspoon salt, and 1/8 teaspoon pepper.
3. Lightly spoon flour into a dry measuring cup; level with a knife. Place flour in a large saucepan; gradually add milk, stirring with a whisk. Cook and stir over medium heat until mixture comes to a boil; reduce heat and simmer 2 minutes, stirring constantly. Remove from heat; stir in cottage cheese, Parmesan, nutmeg, 1/4 teaspoon salt, and 1/8 teaspoon pepper.
4. Spread 1/2 cup white sauce in bottom of an 11- x 7-inch baking dish coated with cooking spray. Arrange 3 noodles over sauce; top with half the vegetable mixture (about 2 cups) and one-third of the remaining white sauce (about 1 cup). Top with 3 noodles, remaining vegetable mixture, half the remaining sauce, and 3 more noodles. Spread the remaining white sauce over noodles. Cover with foil and bake at 400° for 25 minutes. Uncover, sprinkle with mozzarella, and bake an additional 25 minutes or until golden brown. Let stand 15 minutes.