Preheat the oven to 425ºF. On a lightly floured or cornmeal-covered surface, roll the pizza dough out into a 12-inch shape; spread out on a pizza stone or on to a sheet tray. Brush 1/2 cup of the pesto evenly over the dough, leaving at least a half-inch border around the edges. Top the pizza with mozzarella, tomatoes, and any additional toppings. Brush the border with extra virgin olive oil. Bake on a sheet pan or pizza stone in the middle of the oven until the dough is golden brown, 11-12 minutes. Remove from the oven and brush with additional pesto. Allow the pizza to rest for 3 - 4 minutes before serving.
To grill the pizza:
Heat a grill or grill pan over high heat. If using a gas grill, leave one side off. If using a charcoal grill, pile coals on one side.
Roll out the pizza dough or unwrap preformed shell and place on a flour or cornmeal dusted cookie sheet. Oil the grill grates and slide on pizza dough. Cover the grill and allow dough to cook until browned with some visible grill marks, anywhere from 1 to 5 minutes depending on the grill.
Using a pair of tongs, remove the dough to a freshly fkoured cookie sheet with the grilled side is now facing up. Top the pizza using the above instructions and slide back on to grill. Cook until bottom is browned and cheese is melted. If bottom is browning too fast, move the pizza to the cooler side of the grill until cheese is melted.