Heat broiler. Place the tomatoes cut-side up on a broiler-proof baking sheet. Drizzle with 1 teaspoon of the oil and sprinkle with 1⁄8 teaspoon each salt and pepper. Broil until tender, 2 to 3 minutes.
Meanwhile, heat the remaining teaspoon of oil in a large nonstick skillet over medium heat. Crack the eggs into the pan and cook, covered, to the desired doneness, 2 to 4 minutes for slightly runny sunny-side-up eggs.
Transfer the eggs to plates and sprinkle with the scallions, Parmesan, and 1⁄8 teaspoon each salt and pepper. Serve with the tomatoes.