To prepare vegetables, cut bell peppers in half lengthwise; discard seeds and membranes. Place pepper halves, skin sides up, on a foil-lined baking sheet; flatten with hand. Broil 15 minutes or until blackened. Place in a zip-top plastic bag; seal. Let stand 15 minutes. Peel; set aside.
Preheat oven to 450°.
Combine oil, salt, 1/2 teaspoon black pepper, squash, and onion on a baking sheet; toss well. Bake at 450° for 20 minutes. Remove from oven; combine squash mixture and garlic in a bowl.
Decrease oven temperature to 375°.
To prepare cheese mixture, combine cottage cheese and next 3 ingredients (cottage cheese through oregano) in a bowl.
To prepare white sauce, place flour in a medium saucepan. Gradually add milk; stir with a whisk. Place over medium heat. Cook until thick; stir constantly. Remove from heat; stir in 2 tablespoons chopped basil and 1/4 teaspoon black pepper.
Spread 1/4 cup white sauce in bottom of a 13 x 9-inch baking dish coated with cooking spray. Arrange 3 noodles over sauce; top with 1 1/4 cups cheese mixture, 1 cup spinach, 4 bell pepper halves, 2 cups vegetable mixture, and 1/4 cup white sauce. Repeat layers, ending with noodles. Spread remaining white sauce over noodles. Cover and bake at 375° for 15 minutes. Uncover; sprinkle with mozzarella cheese. Bake an additional 20 minutes. Garnish with basil sprigs, if desired.