Melt the butter in a nonstick skillet over medium heat. Score the edges of the pork roll slices 3-4 times (to keep them flat while cooking). Add to the skillet, and cook until lightly browned on both sides, about 6 minutes. Transfer to a paper towel-lined plate to absorb any excess grease.
Reduce heat to medium-low and crack the eggs into the skillet; season with salt and pepper. After 1-2 minutes, gently flip to cook other side (for over-easy). Immediately top each with one slice of cheese; cover and let melt, about 30 seconds. Cook until eggs have reached desired level of doneness.
On the bottom half of each potato roll, place 2-3 slices pork roll, fried egg with cheese, ketchup (if desired), and top half of roll.
Serve and enjoy!