Heat oven to 500 degrees F. Coat a 14-inch pizza pan with nonstick cooking spray.
Heat olive oil in a large nonstick skillet over medium-high heat. Stir in garlic, broccoli rabe, red pepper, onion, mushrooms, salt and pepper. Cook for 4 minutes, stirring occasionally.
On a lightly floured surface, roll out dough into a 14-inch circle. Gently roll up onto a lightly floured rolling pin and unroll onto prepared pizza pan.
Spread sauce over dough to within 1/2 inch of edge. Sprinkle 1-1/2 cups of cheese over sauce. Evenly spoon the vegetables over cheese. Scatter the remaining cheese over vegetables. Bake at 500 degrees F for 18 to 20 minutes or until nicely browned on bottom.
Cool slightly and cut into 8 slices; serve.