Heat grill. In small microwave-safe bowl, combine broccoli and 3 tablespoons water; cover with microwave-safe plastic wrap. Microwave on HIGH for 2 to 3 minutes or until broccoli is bright green. Drain; set aside.
Cut 18x12-inch sheet of heavy-duty foil; spray with nonstick cooking spray. Unroll dough; place on sprayed foil. Starting at center, press out dough with hands to form 13x9-inch rectangle. Brush dough with 1 teaspoon of the oil. Brush squash with remaining teaspoon oil.
When ready to grill, place squash on grill. Invert dough onto grill rack and peel off foil. Cook on gas grill over medium-low heat or on charcoal grill 4 to 6 inches from medium-low coals for 3 to 5 minutes or until bottom of dough is golden brown and squash is crisp-tender and grill-marked, turning squash occasionally.
Remove squash from grill; place on cutting board. Cut squash into bite-sized pieces. Turn dough; grill 1 to 2 minutes or until bottom is set. Carefully remove from grill. Top crust with pizza sauce, tomatoes, squash and broccoli. Sprinkle with cheese.
Return pizza to grill. Cook an additional 3 to 5 minutes or until crust is browned and thoroughly cooked, and cheese is melted.