Heat oil in a large nonstick skillet over medium-high heat.
Add zucchini, onion, and carrot; saut 8 minutes or until lightly browned.
Remove from heat; stir in corn, basil, 1/4 teaspoon salt, and 1/8 teaspoon pepper.
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.
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.