Heat oven to 425°F. Brush a 9–10 inch cast-iron skillet or deep pie dish with 1 tsp oil and dust with cornmeal.
Warm 1 tbsp oil in a skillet over medium-high heat. Cook sausage, breaking it up, until browned and cooked through. Transfer to a bowl.
Add remaining oil to the skillet. Sauté onion, bell pepper, and mushrooms with a pinch of salt until tender, 5–6 minutes.
Stir in garlic, oregano, and red pepper flakes. Cook 30 seconds. Return sausage to pan and season with salt and black pepper to taste.
Stretch dough into a 12-inch round. Press into prepared pan, letting the edges climb up the sides to form a rim.
Scatter half the mozzarella over the dough. Spoon on pizza sauce. Add sausage–veggie mixture and pepperoni. Top with remaining mozzarella and Parmesan.
Brush exposed crust with a little oil. Bake 24–28 minutes, until crust is deep golden and cheese is bubbling.
Let rest 10 minutes. Sprinkle with basil, slice, and serve warm.