Cut four 1-inch slits around the edge of each bologna slice.

Fry the bologna in a dry skillet over medium-high heat for 1 to 2 minutes per side until browned and curled at the edges.

Transfer the bologna to a plate and melt the butter in the skillet.

Fry the eggs over-medium, season with salt and black pepper, and cook until they reach 160°F.

Place one American cheese slice over each egg and cover for 30 seconds.

Fill each roll with two bologna slices and one cheesy egg.