Sprinkle the active yeast in the cup of warm water and let it rest for 5-10 minutes, until the yeast is foaming on top.
In a stand mixer fitted with the dough hook, add in the flour and salt.
Once the yeast is ready, add to the flour mixture and add in the olive oil as well.
Kneed the dough until it all comes together and pulls away from the sides of the bowl. Place the dough in an oiled bowl, and cover with a clean kitchen towel. Place it in a warm spot and let it rise for about 1.5 hours, or until doubled in size.
As the dough is rising, make the balsamic reduction. Bring the balsamic vinegar to a simmer over medium heat. Let it simmer until it's thickened and reduced to about 1/4 cup. Let it cool.
Once the pizza dough is done preheat the oven to 450°.
Punch down the pizza dough and divide it into two. This recipe will make two 10' pizzas.
Roll out the dough on a floured surface. Place the dough on a baking sheet. Brush the pizza dough with olive oil.
Sprinkle the mozzarella cheese all over the pizza. Or arrange fresh mozzarella rounds on the pizza.Arrange the peaches around the whole pizza evenly. Repeat to make the second pizza.
Bake the pizzas for 10-15 minutes. The crust should be lightly golden, and the cheese browning.
Remove the pizza from the oven and let it cool for a few minutes. Drizzle the balsamic reduction on the pizza and spread out the fresh basil.
Cut the pizza into 8 slices and enjoy!