Preheat the oven to 350°F. Line a standard baking sheet with parchment paper. Set aside.
Use a sharp paring knife to hollow out the center from the frozen rolls. Leaving a 1/2-inch order. Using your fingers press the interior of the rolls as flat as possible. (Pop the centers of the bread into a plastic storage bag and refreeze to use as breadcrumbs for another recipe.).
Brush the rolls with melted butter reserving some for after baking.
Sprinkle around 1 tsp of shredded cheese into the bottom of each roll. Top with a single slice of Canadian bacon. Press down.
Crack the egg into a measuring cup and carefully pour into the center. Don't panic if some overflows.
Sprinkle with salt and black pepper to your taste then top with the remaining shredded cheese.
Bake for 15-20 minutes or until the eggs are cooked to your preferred level of firmness..
Brush with remaining butter and serve immediately.
When using large eggs for these rolls, some of the egg white may overflow. It will cook when in the oven, so don't panic. Otherwise, use medium eggs.