Preheat the grill and set the oven rack about 15cm from the heat source.
Heat the oil in a large, oven-proof frypan over medium heat; add the garlic and cook until lightly browned, about 1 minute. Stir in the prawns and the tomatoes. Cook just until the prawns turn pink, 3 to 5 minutes. Pour in wine; simmer for 2 additional minutes.
Top prawns with mozzarella cheese and grill until the cheese is melted and golden. Sprinkle with Parmesan cheese and dried parsley before serving.