1Grate the potatoes and, using cheesecloth, squeeze out as much liquid as possible.
2Add the oil to a large nonstick skillet on medium-high heat. Add the potatoes to evenly cover the bottom of the skillet. Press down with spatula to get potato mixture as flat as you can. Cook for 2 or 3 minutes until the potatoes are brown. Carefully flip the potatoes and cook for a few more minutes. Remove from the skillet onto paper towels. Set aside.
3Reduce the heat to medium-low and add 1 tablespoon of butter. When the butter’s melted crack in the two eggs. Arrange the Canadian bacon slices around the eggs in the skillet. Cook for 2 or 3 minutes and then add the slice of cheese on top of each egg. Flip the bacon.
4Meanwhile put the muffins in the toaster. Keep cooking eggs for 2 or 3 more minutes until the egg whites are set. When the muffins pop from the toaster, build the sandwiches.