These satisfying sandwiches will keep you full until lunchtime.
Crack large eggs into 2 small bowls (1 egg per bowl). Add 1 pinch salt and 1 pinch pepper to each bowl.
Use pastry brush to spread melted butter evenly over cut sides of rolls. Add rolls, buttered side down, to 10-inch nonstick skillet.
Cook rolls over medium heat until cut sides are golden brown, 3 to 5 minutes. Use spatula to transfer rolls, cut sides up, to serving plates.
Add oil to now-empty skillet. Increase heat to medium‐high and heat oil for 30 seconds (oil should be hot but not smoking).
Working quickly, pour eggs into opposite sides of skillet. Cover skillet with lid and cook for 1 minute. Turn off heat and slide skillet to cool burner. Carefully flip eggs.
Place 1 slice cheese on top of each egg. Cover skillet and let sit for about 1 minute for slightly runny yolks or about 2 minutes for set yolks.
The ideal fried egg—with a cooked white and a runny yolk—can be tricky to make because egg whites and egg yolks set at different temperatures. Egg whites are fully cooked at 180 degrees, while egg yolks begin to thicken at 150 degrees and are fully set at 158 degrees.
One way to get fully set whites without overcooking the yolks? Steam. In this recipe, we cover the skillet with a lid while the eggs cook—this traps steam and heats the eggs from the top and the bottom.