Heat oven to 400°F. In 6-inch nonstick skillet, cook sausage over medium-high heat 4 to 6 minutes, stirring frequently, until no longer pink. Stir in mushrooms, tomatoes and pizza sauce. Remove from heat; cover to keep warm.
Spray bottom and side of 12-inch cast-iron skillet or other ovenproof skillet with cooking spray. Unroll dough in skillet; press in bottom and at least halfway up side. Bake 5 minutes. Sprinkle 1 3/4 cups of the cheese over dough. Spoon sausage and vegetable mixture over cheese; top with remaining 1/4 cup cheese.
Bake 15 to 18 minutes or until crust is golden brown. Sprinkle with green onions. Let stand 10 minutes before cutting. To serve, cut into 6 wedges.