
Make the sun-dried tomato topping.
Prepare the rolls: Split the rolls, toast them, and spread each side with pesto. Place each roll on a plate and top one side with two slices of prosciutto, arugula, and a 1-ounce slice of fresh mozzarella. Spoon the sundried tomato salsa over the mozzarella and set aside.
Cook the eggs: In a medium skillet, add 2 teaspoons olive oil. Once the oil begins to shimmer, crack the eggs into the pan. Fry on one side for about 2 minutes, carefully flip the egg and fry for another 1 to 3 minutes, depending upon how set you prefer your yolks. Season with salt and pepper.
Finish and serve: Add an egg to each roll, top with about 2 tablespoons of sun-dried tomato topping, cover with the other half of the roll, and serve!