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Heat tomatoes, vodka, and cream in a small saucepan over medium heat until bubbling and vodka smell is cooked off, about 15 minutes. Season as desired with salt and freshly ground pepper and set aside to cool.
Meanwhile roll pizza dough to a 12-inch round. Drizzle olive oil on a baking sheet to coat and place dough on top. Pierce the dough in several places to prevent it from bubbling up unevenly. Spread sauce evenly over the dough. Evenly distribute mozzarella across pizza and scatter whole basil on top. Drizzle with oil and bake until crisp is crusty, cheese is melted, and underside of dough is golden brown, about 20 minutes.