1. Cut blocks of cheese into 1-inch cubes. Arrange cheese cubes and tomato halves in an 8-inch square baking dish.
2. Whisk together 1/2 cup olive oil, chopped parsley, and next 6 ingredients; pour evenly over cheese cubes. Cover and chill at least 8 hours or up to 24 hours. Transfer mixture to a serving plate. Garnish with fresh flat-leaf parsley sprigs, or spear tomato halves and cheese cubes with short rosemary stems, if desired. Drizzle with marinade, if desired.