Cook pasta according to package directions.
In a large bowl, combine the eggplant, zucchini, squash, onion, oil, garlic, salt and pepper. Transfer to two 15x10x1-in. baking pans coated with cooking spray. Bake at 425° for 20-25 minutes or until tender.
Meanwhile, in a large skillet, cook beef over medium heat until no longer pink; drain. Stir in the tomato puree, Italian seasoning and brown sugar.
Drain pasta; stir in tomato mixture and roasted vegetables. Sprinkle with cheese.