1 russet potato, peeled
4 slices bacon (thick-sliced works the best)
4 slices white bread
2 tablespoons butter, very soft
6 ounces sharp cheddar cheese, shredded
1. Place peeled potato in a small saucepan, cover with cold water and bring to a boil over high heat. Once it reaches a boil, reduce the heat and simmer for 5 minutes. Remove from heat and let sit for 15 minutes.
2. Meanwhile, fry the bacon in a large (12-inch) cast iron skillet (use stainless steel if you don't have cast iron) until crisp. Remove from the skillet to a paper-towel lined plate to drain. Pour the bacon drippings from the pan into a small bowl and set aside.
3. Return the pan to the burner (do not wipe out the pan) over medium heat and fry the eggs to your desired degree of doneness (you can cook them the whole way through, leave the yolk runny, whatever your preference). Remove the eggs to a small plate and cover with foil to keep warm.
4. Once the potato is cool enough to handle, grate with the large holes of a box grater. Heat your skillet over high heat and then measure the reserved bacon drippings. Add 2 tablespoons to the hot skillet (if you don't have quite 2 tablespoons, use vegetable or canola oil to make up the difference). Spread the shredded potatoes in a thin, even layer over the bottom of the skillet. Season with salt and pepper and cook for 5 minutes, or until golden brown on the bottom. Don't try to turn them or move them until the 5 minutes is up! Once brown, use a wide spatula to flip the potatoes over and cook on the other side for 3 to 5 minutes, or until golden brown as well. Once finished, remove the hash browns to a plate.
5. Reduce the heat to medium-low. Butter all of the slices of bread, making sure to spread the butter over the entire surface of the bread to the edges. Place two pieces butter-side down in the skillet, and then top each slice of bread with a quarter of the cheese, half of the potatoes, one egg, two slices of bacon and the remaining cheese. Top with another slice of bread, buttered side-up. Cook until the bottom is golden brown, then carefully flip the sandwich and continue to cook until golden brown on the other side, about 5 to 7 minutes total. Slice in half and serve!