Remove dough from refrigerator and let stand 1 hour (do not remove from bag until stand time is complete).
Preheat oven to 350°F. Cut tomatoes in half, then combine with oil, 1 teaspoon oregano, salt, and pepper until evenly coated. Place tomatoes on baking sheet; bake 8–10 minutes until they begin to release their juices. Remove from oven and let stand to cool.
Increase oven temperature to 400°F. Flour hands lightly and pat dough evenly into lightly greased (or nonstick) pizza pan (or turn dough out onto a lightly floured surface and roll to desired thinness). Spread tomato sauce over dough; top with tomatoes. Slice cheese and arrange over top of pizza.
Bake pizza 18–25 minutes (depending on thickness of pizza) until crust is golden and cheese is melted. Let stand 5 minutes. Tear basil leaves (¼ cup); top pizza with basil and remaining 1 teaspoon oregano. Slice and serve.