Set a 10-inch skillet or dark nonstick frying pan over medium heat.
Split the roll in half across the beltline and spread each cut face with about 1/2 tablespoon of the butter. Place roll cut-sides down onto the skillet and cook until lightly toasted. Set aside.
Melt remaining tablespoon of butter in the skillet.
Make three small, evenly-spaced slits around the perimeter of each slice of the pork roll to prevent them from curling up as they cook.
Add pork roll to skillet and cook, pressing with a spatula from time to time to flatten and flipping once or twice, until warmed through and lightly browned on both sides. Drain on paper towels.
Crack the eggs into a small mixing bowl and add the salt and pepper. Beat with a fork until homogenous.
Pour the scrambled eggs into the skillet. Cook, dragging the edges to the center from time to time and swirling the pan once in a while to encourage the uncooked top parts to wend their way to the bottom.
When egg is just about cooked, place the cheese slices on top to cover the surface and let them melt a bit.
To assemble the sandwich, place the pork roll and then the cheese-covered eggs onto the bottom half of the roll and top with the other half of the roll.
For an authentic experience, you'll want the sandwich to steam a bit before serving. Wrap it in deli paper (or parchment or wax paper if that's what you've got) before cutting in half. Then wrap the whole thing in foil. Let it rest for five minutes before serving (with ketchup and hot sauce, if you like).