In a large shallow glass dish, arrange the cheese in a single layer. In a small bowl, whisk together the oil, lemon juice, hot sauce (if using), garlic, dried oregano and pepper. Pour the mixture evenly over the cheese. Let marinate at room temperature for one hour or in the refrigerator for up to one day. Preheat a gas grill on medium-low. Remove the cheese from the marinade, reserving the marinade. Grill the cheese with the lid down, turning once, until it is soft and develops nice grill marks, 5 to 7 minutes per side.
Arrange the cheese on a serving platter. Pour over the leftover marinade. Scatter the tomato slices on or around the cheese. Drizzle with oil and a bit of lemon juice. Sprinkle the tomatoes lightly with a bit of salt (if using). Sprinkle with the fresh oregano. Serve immediately.
Makes 4 to 6 servings