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.
Use a sharp, potent cheese in this dish for the most flavor. Parmesan, Romano, Asiago, or sharp cheddar will all work as well in the filling. Stick to mozzarella for the top, however, as it melts and browns the best. For extra browning, place the lasagna under the broiler for a minute or two at the end of cooking.