Preheat oven to 450 degrees F. Place the pizza stone in the oven while it is heating up. The pizza stone has to be in there for at least 30 minutes. Keep the pizza stone in there until you are ready to add your toppings on the pizza.
Meanwhile, slice the mozzarella and shred the parmesan cheese. Mince the garlic and combine it with the olive oil in a small bowl. Cut the peaches in half and remove the core. Slice into pieces about 1/4" thick. Tear proscuitto into bite-sized pieces. Set aside.
Lightly flour a piece of parchment paper. Place your dough on the parchment paper and roll it out until it is about 12" in diameter.
Carefully take the pizza stone out of the oven and sprinkle with cornmeal. Add your shaped pizza dough directly on top. (Alternatively, instead of using cornmeal directly on the stone, you can put the dough with the piece of parchment directly on the stone.)
Use a pastry brush to cover the entire surface of the dough in olive oil/garlic (not just the edges). Season with salt and pepper. Place the prosciutto pieces on the pizza followed by the mozzarella, parmesean, and peach slices. Place back in oven and bake for 10-12 minutes until the crust is golden brown.
While the oven is baking, thinly slice the basil. (See recipe notes.)
When the pizza comes out of the oven, tranfer it to a cutting board. Add dollops of burrata, the thinly sliced basil, and a healthy drizzle of balsamic glaze. Slice and serve!