1.
Assemble ingredients. Preheat grill to medium-high. Use your hands to knead and roll out dough on a lightly floured surface or parchment paper. Brush one side of each pizza with olive oil. Set pizza dough on grill, oiled side down, and cook with grill open until bottom is seared and cooked, about 4 to 5 minutes. Top should still be slightly doughy. Bubbles may form but will deflate when dough is turned.
2.
Remove dough from heat and flip so grilled side faces up. Brush lightly with olive oil and spread a thin coat of pesto over pizzas. Next, top with tomatoes and mozzarella. Return pizza to grill, close and cook until cheese is thoroughly melted and lightly browned in spots. Remove from heat, garnish with fresh basil and serve immediately.