Mix bread flour, water, 3 tablespoons olive oil, yeast, and salt together in a large bowl; when the dough pulls together, turn it out onto a lightly floured surface and knead until smooth and elastic, about 8 minutes.
Place dough in a large, lightly-oiled bowl and turn to coat. Cover with a towel and let rise in a warm place for 2 hours.
Preheat an oven to 450 degrees F (230 degrees C). Lightly grease 2 14-inch pizza pans with 1 teaspoon oil; lightly dust each pan with cornmeal.
Divide dough in half and roll out into 2 thin rounds. Transfer each round to a prepared pizza pan.
Spread pizza sauce over dough; top with mushrooms, peppers, onions, olives, and oregano. Drizzle with 1 tablespoon olive oil.
Bake pizzas in the preheated oven until crust is golden and sauce is bubbling, about 20 minutes. Garnish with crushed red pepper.