Coat a large nonstick skillet with cooking spray; place over medium-high heat until hot. Add zucchini, red pepper, and mushrooms. Cook, stirring constantly, 5 minutes. Stir in 1/2 cup pizza sauce; set aside.
Roll crust into a 15- x 10-inch rectangle; cut into 4 (7 1/2- x 5-inch) rectangles.
Spoon one fourth of vegetable mixture onto one end of each rectangle; sprinkle evenly with mozzarella cheese. Fold rectangles in half over filling; press edges together with a fork. (At this point pockets may be covered and refrigerated to bake later for 12 minutes. Or, assemble pockets, bake 6 minutes, and freeze. Thaw in refrigerator overnight before baking the remaining 6 minutes or until browned.)
Coat tops with cooking spray, and sprinkle with Parmesan cheese. Place on a large baking sheet coated with cooking spray. Bake at 400° for 12 minutes or until golden. Serve with remaining 2 cups warm sauce.