Heat the broiler to 355F.
Drizzle oil on the face of tomato and sprinkle with salt, pepper, and a little parmesan, place cut side up under the broiler. Cook for 3 – 4 minutes until soft, while these are cooking.
Heat remaining oil in a medium skillet over medium heat, break the eggs and place into the skillet, cover and cook until your desired liking.
Transfer eggs and tomatoes to serving plate, sprinkle with remaining parmesan, scallions, salt and pepper to taste.