Roll the pizza dough into a ball, then place in a large bowl and cover tightly with plastic wrap. Let rest at room temperature for 30 minutes. Dough will rise slightly.
In the meantime, heat the grill to 400 F. If working with a gas grill, leave one burner off or on low. Place the sliced peaches on the grill and grill for 1–2 minutes per side, until each side has char marks and peaches are slightly softened, but not mushy. If using a gas grill, place over indirect heat. Remove from the heat and set aside.
Stretch the pizza dough into a 16-inch circle, pinching the perimeter into a thick crust. Brush with oil, then flip and brush oil all over the bottom of the crust in a thin layer.
Place the pizza on the grill bottom-side down and grill until the top begins to bubble, about 5–7 minutes. The dough will be rising and lightly charred underneath. Flip, carefully, and cook the other side until lightly charred and no longer doughy, about 4–5 minutes.
Flip again so that the side with the crust faces up. Add the mozzarella and gorgonzola to the middle of the pizza and cook until cheese has melted, about 10 minutes. Remove from the heat.
While warm, top with arugula and grilled peaches, then drizzle with hot honey. Cut into 8–10 pieces and serve immediately.