Heat the oven to 425 degrees F and arrange and a rack in the middle.
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 black 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 cheese is melted, and underside of dough is golden brown, about 20 minutes.