For 4 servings:
Follow Instructions for Grilled Pizza, removing the pizzas from the grill after grilling 30 seconds on the second side. In a bowl, mix tomatoes, basil, 1/4 cup oil and the garlic. In a separate bowl, mix the two cheeses. Spread some cheese mixture over each pizza, then dollop each with the tomato mixture. Do not spread. Sprinkle each with parsley, place back on the grill. Close the lid and cook just till cheese is melted, about another minute. Serve immediately, using remaining oil to drizzle over top, as desired.