Score the edges of the pork roll slices in 3 or 4 places. This will keep the slices flat and prevent them from buckling as they cook.
Heat the butter in a large nonstick skillet over medium-high heat. Add the pork slices in one layer and brown well on both sides, about 6 minutes. Remove the slices and place one on top of each toasted roll bottom.
Reduce the heat to medium-low and crack the eggs into the skillet. Break each yolk with the corner of your spatula. Sprinkle with salt and pepper. After about 2 minutes, flip the eggs and continue cooking on the other side. Immediately place a slice of Cooper Sharp cheese on top of each egg. Cover with a lid for about 30 seconds to melt the Cooper cheese.
Place each egg with cheese on top of a browned pork roll slice, then complete the sandwiches with the kaiser roll tops.