Cut peppers in half lengthwise; remove and discard seeds and membranes. Place peppers, skin sides up, on a baking sheet, and flatten with palm of hand. Broil 5 1/2 inches from heat (with electric oven door partially opened) 15 to 20 minutes or until charred. Place in ice water until cool; peel and discard skins. Slice peppers into thin strips.
Arrange garlic cloves and potato in a single layer on a large baking sheet; bake at 400° for 30 minutes or until potato is tender. Remove from oven; let cool. Peel garlic cloves.
Coat a large nonstick skillet with cooking spray; add oil. Place over medium-high heat until hot. Add onion, and saute 5 minutes or until tender. Add mushrooms and garlic; saute 2 minutes. Add wine and water.
Combine milk and flour; stir well with a wire whisk. Add flour mixture to mushroom mixture in skillet; bring to a boil, and cook 5 minutes or until thickened and bubbly. Stir in parsley, and set aside.
Press spinach between paper towels to remove excess moisture. Combine spinach, ricotta cheese, cottage cheese, Parmesan cheese, salt, and pepper in a medium bowl; stir well, and set aside. Combine roasted pepper strips, squash, and broccoli; stir well, and set aside.
Coat a 13- x 9- x 2-inch baking dish with vegetable cooking spray. Spread 1/4 cup mushroom sauce in baking dish. Arrange half of potato slices over mushroom sauce. Spread half of cheese mixture over potato. Arrange half of broccoli mixture over cheese mixture, and top with half of remaining mushroom sauce. Repeat layers with remaining potato slices, cheese mixture, broccoli mixture, and mushroom sauce. Top with mozzarella cheese. Cover and bake at 350° for 30 minutes. Uncover and bake 15 additional minutes. Let stand 10 minutes before serving.