1/3 cup slightly packed fresh basil leaves , chopped
Place pizza stone in oven and preheat oven to 450 degrees. Let pizza stone preheat with oven and rest 30 minutes (assemble pizza during last 10 minutes or so).
Meanwhile, pour balsamic vinegar and honey into a large and deep skillet. Set skillet over medium heat, allow mixture to cook and simmer, until reduced to slightly under a 1/2 cup, about 15 minutes (I recommend using a silicone spatula to stir, so you can scrape bottom and sides of pan while stirring. Stir mixture occasionally during first 5 minutes, then stir constantly during last 10 minutes).
Lightly dust a sheet of parchment paper (about 14-inch long) with flour. Stretch and shape dough into a 12 1/2-inch round. In a small bowl, stir together olive oil and garlic. Brush mixture evenly over top of crust, working to evenly distribute garlic. Season crust lightly with salt and pepper.
Layer prosciutto over crust into an even layer, aligning pieces side by side (if they overlap slightly that's fine). Dollop small portions of the ricotta over pizza, then sprinkles with mozzarella cubes and asiago cheese.
Cut peaches in half and core. Laying peaches with sliced side down, cut peaches into slices (slightly over 1/4-inch thick). Layer peaches evenly over pizza. Using a pizza peel, transfer pizza on parchment to preheated pizza stone in oven. Bake 10 - 12 minutes until edges are lightly golden.
Remove from oven, sprinkle with fresh basil, and drizzle with honey balsamic reduction (store left over reduction in fridge). Cut into slices and serve warm.