Top each muffin half with tomato; set aside. In a small nonstick skillet, heat oil over medium-low. Gently crack eggs into skillet; cook until whites are almost set, 1 to 2 minutes.
Top each egg with a slice of cheese; cover skillet for 1 minute. Slide one egg onto each muffin; season with salt and pepper.
This was fabulous with a ripe, meaty tomato. I've made it since with winter tomatoes and added pesto or fresh basil (whatever I've had on hand) to boost the flavor. Very easy and a wonderful way to highlight great tomatoes.