1In a cast iron or heavy skillet, cook bacon over medium heat until crispy, about 8–10 minutes. Transfer to a paper towel and chop into bite-sized pieces.
2Drain all but 1 tbsp of bacon grease from the skillet. Add 2 tbsp vegetable oil and increase heat to medium-high.
3Add shredded potatoes and diced onion to the hot oil. Press gently with a spatula. Let cook undisturbed for 4–5 minutes until the bottom is golden, then flip in sections and cook another 4–5 minutes until golden throughout. Season with salt and pepper. Transfer to a plate.
4Reduce heat to medium. Add butter to the same skillet.
5Crack eggs into the skillet and cook to your preference: sunny-side up (3–4 minutes), over-easy (4–5 minutes), or over-hard (5–6 minutes). Season with salt and pepper.
6Divide hash browns between two plates, top with eggs, scatter chopped bacon over everything, and serve immediately.