Vegetable lasagna is a crowd-pleaser and a classic make-ahead dish. You can use precut onions, matchstick-cut carrots, and broccoli, in addition to precooked noodles, to speed up preparation. If you make it ahead, let it cool completely, then cover and chill. The next day, heat single servings in the microwave. Freeze leftovers for dinner.
Preheat oven to 375°.
Heat a large Dutch oven over medium-high heat. Coat pan with cooking spray. Add onion to pan; sauté 4 minutes or until lightly browned. Add garlic; sauté 1 minute. Spoon onion mixture into a large bowl.
Heat 1 teaspoon oil in pan over medium-high heat. Add zucchini and yellow squash; sauté 4 minutes or until tender and just beginning to brown. Add to onion mixture.
Heat remaining 1 teaspoon oil in pan over medium-high heat. Add sliced carrot; sauté 4 minutes or until tender. Add chopped broccoli; sauté 4 minutes or until crisp-tender. Add to onion mixture. Sprinkle with 1/2 teaspoon salt; toss well to combine.
Place flour in a medium saucepan. Gradually add milk, stirring with a whisk until blended. Bring to a boil over medium heat; cook 2 minutes or until thick, stirring constantly. Remove from heat. Add 1/2 cup Parmesan, remaining 1/2 teaspoon salt, pepper, and nutmeg; stir until smooth. Stir in spinach.
Combine cottage cheese and 1 1/2 cups mozzarella; stir well. Spread 1/2 cup spinach mixture in bottom of a 13 x 9-inch baking dish coated with cooking spray. Arrange 4 noodles over spinach mixture in dish; top with half of cottage cheese mixture (about 1 1/2 cups), half of vegetable mixture (about 2 1/2 cups), and about 1 cup spinach mixture. Repeat layers, ending with noodles. Spread remaining spinach mixture over noodles; sprinkle with remaining 1/2 cup Parmesan and remaining 1/2 cup mozzarella.
Cover and bake at 375° for 20 minutes. Uncover and bake an additional 20 minutes or until cheese is bubbly and beginning to brown. Let stand 10 minutes before serving.