Peel and chop the potatoes into approximately 1 inch cubed pieces.
Bring a pot of water to boil. Add the potatoes and boil until you can easily insert a knife into a piece. You want the potatoes to be tender, but to also hold their shape. Drain the potatoes and set them aside.
Preheat oven to 350 degrees Fahrenheit.
Heat a large pan to medium heat. Add the bacon. Cook until the bacon starts to render some fat and just begins to crisp up on the edges.
Add the potatoes to the pan, followed by the butter, oil, salt, and pepper. Give it a good stir.
Crack the eggs and add them to the skillet. I cracked each egg into a small bowl first and then slid it into the skillet. Sprinkle the eggs with a little extra salt and pepper.
Drizzle the dish with shredded cheddar cheese.
Bake for 14 to 16 minutes, or until the egg whites are completely set.