Thirty minutes before baking, preheat the oven to 500°F. Place a pizza stone on the bottom rack of the oven and heat for at least 30 minutes.
On a floured surface, divide the dough into 2 pieces and form into balls. Roll 1 piece of dough into a 10- to 11-inch circle, 3/8 inch thick. Transfer to a heavily floured pizza peel. Top with half of the smoked mozzarella cheese, distributing evenly. Slide the pizza onto the pizza stone and bake until golden and crisp, 8 to 12 minutes.
In the meantime, whisk together the oil, vinegar, and garlic in a bowl to make a vinaigrette. Season with salt and pepper. Add the yellow and red cherry tomatoes and toss together.
When the pizza is done, place on a platter. Top with half each of the tomatoes, vinaigrette, and basil. Serve immediately.
Make a second pizza with the remaining ingredients.