Step 1 Preheat oven to 350°F (180°C). Line baking sheet with parchment paper; set aside. Halve rolls horizontally; set tops aside.
Step 2 Hollow out bottom of rolls, leaving about 1/2-inch (1 cm) border all around. (Reserve hollowed-out bread for another use.) Place bread bowls on prepared pan.
Step 3 Arrange slice of ham in bottom of each bowl. Crack 1 egg into each bread bowl. Season with salt and pepper; top with cheese.
Step 4 Bake until cheese is melted, egg whites are set and yolks are cooked to desired doneness, approximately 20 to 25 minutes. Add reserved tops to baking sheet during last 5 minutes of baking time. Top with salsa and serve with toasted tops.