Preheat the oven to 250 degrees . In a large skillet, heat 1 1/2 teaspoons olive oil over medium heat. Add 2 bread slices and cook, turning once or twice, until golden on both sides, about 4 minutes. Transfer the bread to a baking sheet. Repeat with 1 1/2 teaspoons olive oil and the remaining 2 bread slices. Rub the toast lightly with the garlic and spread the goat cheese on top. Keep warm in the oven.
Heat 1 tablespoon olive oil in the same skillet, add the tomato slices, season lightly with salt and pepper and cook, turning once, until softened, about 8 minutes. Arrange the tomatoes on top of the toasts and return to the oven. Wipe out the skillet.
Heat the remaining 1 tablespoon olive oil in the same skillet. Crack the eggs into the pan, season lightly with salt and pepper, cover and cook over medium heat to desired doneness. Place the toasts on 4 plates and top each with an egg.