Preheat oven to 375.

Heat a large pot over medium-high heat. Coat with cooking spray. Sauté onion 4 minutes or until lightly browned. Add garlic, sauté 1 minute. Spoon onion mixture into a large bowl.

Add 1 teaspoon olive oil to the same pot. Add zucchini and yellow squash, sauté 4 minutes or until tender and beginning to brown. Add to onion mixture in the bowl.

Add another teaspoon olive oil to pot. Add carrot, sauté 4 minutes. Add broccoli to the carrot, sauté 4 minutes, or until crisp-tender. Add to onion mixture in the bowl.

Sprinkle vegetables with salt and toss to mix well.

Place flour in a medium saucepan. Gradually add milk, stirring with a whisk until well blended. (This is called a roux, pronounced "rue.") Bring to a boil over medium heat, cook 2 minutes or until thick, stirring constantly. Remove from heat.

Add ½ cup Parmesan cheese, remaining ½ teaspoon salt, pepper, and nutmeg to the roux. Stir until smooth.

Add spinach and spaghetti sauce to milk mixture. Stir until well blended.

Combine cottage cheese and 1 ½ cups mozzarella, stir well. Spread ½ cup spinach mixture in the bottom of a 9x13 baking dish coated with cooking spray. Arrange 4 noodles over spinach mixture, top with half of cottage cheese mixture (about 1 ½ cups), half of the vegetable mixture (about 2 ½ cups), and 1 cup of spinach mixture.

Repeat layers, ending with spinach mixture.

Sprinkle with remaining ½ cup Parmesan and remaining ½ cup mozzarella cheese.

Cover and bake at 375 for 20 minutes. Uncover and bake an additional 20 minutes or until cheese is bubbly and top is just beginning to brown.

Let stand 10 minutes before serving.