Heat oven to 450°F. Spray 15x10x1-inch pan with cooking spray. In pan, place bell peppers, summer squash, onion and mushrooms in single layer. Spray vegetables with cooking spray; sprinkle with salt and pepper. Bake uncovered 15 to 20 minutes, turning vegetables once, until crisp-tender.
Meanwhile, spray 13x9-inch (3-quart) baking dish with cooking spray. Cook and drain noodles as directed on package using minimum cook time. In medium bowl, crumble chèvre into pesto; stir.
Spread 1/2 cup pasta sauce in baking dish; top with 3 noodles. Layer with half the pesto mixture and 2 cups of the vegetables. Top with 3 more noodles. Top with 3/4 cup sauce and 1 cup shredded cheese blend. Top with 2 cups vegetables, 3 noodles, remaining half of pesto mixture, 2 cups vegetables, 3 noodles and 3/4 cup sauce. Sprinkle remaining 1 cup shredded cheese over top.
Reduce oven temperature to 375°F. Bake uncovered 20 to 30 minutes or until hot. Let stand 10 minutes before cutting.