Arrange tomato pieces in a large shallow bowl or serving plate.
Sprinkle with the tomatoes with a pinch of coarse salt and a pinch of white sugar if the tomaotoes aren't particularly sweet.
Stir the tomatoes and let them rest at room temperature for 15 minutes.
Drizzle the olive oil and sherry vinegar over the tomatoes. Gently stir to coat.
Finish the salad with a layer of shaved parmesan and fresh basil. Add red peper flakes, coarse salt, and freshly cracked pepper to taste.
Serve at room temperature.