To prepare grilled vegetables, place bell peppers, skin sides down, on a grill rack coated with cooking spray; cook 15 minutes or until blackened. Place in a zip-top plastic bag; seal. Let stand 15 minutes. Peel and cut into strips.
Place squash and onion on grill; cook 5 minutes on each side or until tender.
To prepare tomato purée, place tomatoes in a large Dutch oven. Cover and cook over medium heat 30 minutes or until tender, stirring occasionally. Place tomatoes in a blender or food processor; process until smooth. Return to pan. Stir in vodka; bring to a boil. Reduce heat, and simmer 10 minutes, stirring occasionally. Stir in 1 1/2 teaspoons salt. (You will have 5 cups purée.)
To prepare white sauce, combine flour, 1/4 teaspoon salt, and nutmeg in a medium saucepan; gradually add the milk, stirring with a whisk. Cook over medium-high heat until thick (about 7 minutes), stirring constantly. Set aside.
Bring water to a boil in a large stockpot. Add noodles; return to a boil. Cook, uncovered, 10 minutes or until noodles are done, stirring occasionally. Drain.
Preheat oven to 375°.
Spread 1/3 cup white sauce in bottom of a 13 x 9-inch baking dish coated with cooking spray. Arrange 3 noodles over white sauce; top with one-third of grilled vegetables, 1/3 cup basil, 1/3 cup white sauce, and 1/2 cup tomato purée. Sprinkle with 1/4 teaspoon black pepper, 1/4 cup Gruyère, and 2 tablespoons Parmesan. Repeat layers twice, ending with noodles. Spread remaining white sauce, 1 1/2 cups tomato purée, remaining Gruyère, and remaining Parmesan over noodles. Bake at 375° for 45 minutes or until bubbly and top is browned. Remove from oven; let stand 15 minutes.
Note: You will have 2 cups of leftover tomato purée. Cover refriderate for 1 week or freeze up to 3 months.