Heat your grill to medium. Make sure to oil the grates well; this is crucial to prevent the dough from sticking.
Roll out the pizza dough into a long rectangle. Use a fork to dock the dough. Place it on the oiled grates and cook for 3-5 minutes until it easily comes off the grill and shows distinct grill marks. Flip and cook for another ~3 minutes, then take it off the grill.
While the dough is grilling, place the peach slices on the grill and cook for ~3 minutes on each side.
Spread pesto on top of the pizza dough, then add peaches, tomatoes, burrata, arugula, and basil. Drizzle with olive oil and honey, then sprinkle with salt and pepper. Slice it up and enjoy!