While the potatoes are cooking, in a medium size bowl add the eggs, milk, and a few dashes of pepper. Whisk the eggs and set aside.
Spread butter inside (including the sides) each single serving size skillet, ramekin, or pan, and add the fried potatoes in equal portions. Top with pieces of Canadian bacon.
Whisk the eggs again and pour them over the potatoes. Top with the shredded cheese and bake in the oven for about 15 minutes or until the eggs are cooked and the cheese is melted.