Blend tomatoes, oil, vinegar, garlic, and oregano. Adjust to 2 cups. Season and refrigerate or freeze.
Preheat oven to 500°F. Grease a skillet. Divide dough in half. Roll one piece into an 11-inch round and press into skillet.
Spread sauce, top with mozzarella.
Cook over medium-high until crust puffs and browns, 2 to 4 minutes.
Bake until crust is golden and cheese melts, 7 to 10 minutes.
Cool slightly, top with basil, slice, and serve. Repeat for second pizza.