Prepare Deep-Dish Pizza Dough, and set aside.
Heat oil in a large nonstick skillet over medium heat. Add pepper, onion, and garlic, and sauté 5 minutes. Add mushrooms, oregano, and salt; sauté 3 minutes or until tender. Remove from heat; cool.
Spread half of tomatoes over each prepared crust, and top each with half of vegetable mixture. Sprinkle Monterey Jack cheese and provolone cheese evenly over pizzas.
Bake at 475° for 15 minutes. Reduce oven temperature to 375°, and bake 15 additional minutes. Cut each pizza into 8 wedges.