In a small saucepan, heat water and vinegar. Bring to a boil and stir with a spoon to keep the water moving quickly. Carefully crack eggs into water. Remove from heat and let sit for 4 to 5 minutes.
Meanwhile, brush one side of bread slices with oil and place oil side down in a medium skillet. Sprinkle tops of bread with feta cheese. Toast until cheese is melted and bread is golden brown on the bottom side.
Place tomato on top of the cheese. Using a slotted spoon, carefully remove eggs from water and place on top of tomatoes. Sprinkle with salt and pepper, serve and enjoy!