Preheat oven to 425F. Roll pizza dough out to fit a 12-in pizza pan. Set aside for a moment.
In a small saucepan over medium heat, heat olive oil until shimmery then add garlic and saute 1-2 minutes until fragrant. Add red pepper and basil and cook 1 additional minute.
Remove olive oil mixture from heat and brush all over prepared pizza dough. Arrange mozzarella in a single layer on pizza dough and top with sliced peaches and basil leaves. Season pizza with salt and pepper to taste.
Bake pizza at 425F 25-30 minutes, rotating pan once until crust is a deep golden brown and cheese is browned and bubbly.
While the pizza bakes, pour vinegar in a small saucepan and heat over medium-high heat until simmering. Reduce heat to medium-low and let simmer until balsamic is reduced in half and thickened into a thick glaze.
Drizzle balsamic glaze over pizza and cut into slices. Serve immediately and enjoy!