In a 12-inch skillet heat 1 teaspoon of the oil over medium-low heat. Add snap peas and tomatoes; cook and stir about 4 minutes or until peas are crisp-tender and tomatoes are heated through. Stir in dill. Season to taste with salt and pepper. Remove from skillet; cover and keep warm.
In the same skillet heat another 1 teaspoon of the oil over medium heat. Brush both sides of bread slices with the remaining 2 to 3 teaspoons oil. Cut or tear a hole in the center of each slice, leaving about 1/2 inch of bread around the edges. Place bread slices in hot skillet. Break an egg into the center of each bread slice. Sprinkle with salt and pepper.
Cook, covered, for 2 to 3 minutes or until bottoms of bread are golden. Using a spatula, turn bread over; cook about 2 minutes more or until eggs are desired doneness. Serve with vegetable mixture.