1. Heat a 12-inch heavy stainless-steel or cast-iron skillet over medium heat until hot enough to sizzle a drop of water. Add oil. Arrange tomatoes cut-side down in the pan and cook, uncovered, until just tender and the undersides are darkened, 10 to 15 minutes.
2. Mix parsley and garlic in a small bowl.
3. Using a wide spatula, carefully turn each tomato cut-side up. Reduce the heat to medium-low. Sprinkle each tomato with sugar (if using), salt and pepper, followed by equal portions of the parsley mixture and shredded cheese. Cover and cook until the cheese is melted, about 2 minutes. Serve warm.

Yield: 4 servings