Preheat your grill on high for at least 10 minutes
Sprinkle a large cutting board generously with cornmeal. Place the dough on top, divide into two equal portions, and set one aside. Sprinkle some flour on top to prevent fingers from sticking. Use your fingers to press/stretch each portion out into a roughly ¼-inch thick oblong shape (don’t form a thicker “crust” on the edges, you want it all a uniform thickness). Add more cornmeal or flour if the dough is sticking to the board or your hands. You can use a rolling pin towards the end if you’d like. Don't make it too thin or it will tear. Brush olive oil on one side.
Carefully transfer the dough from the cutting board to the grill, placing the oiled side down. Cover and let cook for 1 minute, or until charred on the bottom and bubbly on top (if your grill tends to run super hot, reduce the heat a bit so it doesn’t get scorched).
Use a spatula to loosen the pizza from the grill grates and transfer the pizza back to the cutting board, flipping it over so that the grilled side is facing up. Add your toppings to the grilled side (spread the pesto all over + top evenly with mozzarella and goat cheese).
Transfer back to the grill. Cover and let cook for 1-2 more minutes, or until the dough is charred on the bottom and toppings are bubbling a bit.
Let cool for about 5 minutes, then scatter the cherries all over. Top with parmesan and black pepper. Use kitchen shears or pizza cutter and cut into rectangles.