Preheat the oven to 500 degrees F or as high as your oven will go. If you have a pizza stone, preheat the stone in the oven for at least 30 minutes to allow it to get thoroughly hot.
Divide dough into tennis-ball sized pieces. Take one piece of dough and punch it down on a lightly floured surface. Roll the dough out into a circle approximately 1/4-inch thin. Place the pizza on a pizza peel or pan that has been generously coated with corn meal. Lightly brush with 1 tablespoon of olive oil. Top with mozzarella, goat cheese, and peach slices. Drizzle the pizza with balsamic vinegar. Repeat for remaining pizzas.
Place the pizza in the oven-directly on the pizza stone, or on the oven rack. Bake for 8 to 10 minutes or until pizza crust is golden and cheese is melted. Remove from oven and top with basil. Cut into slices and serve.