Dice the potato into small, uniform cubes to ensure even cooking and maximum crispiness.
Heat the ghee in a large cast-iron or non-stick skillet over medium-high heat.
Add the diced potatoes to the skillet and cook, stirring occasionally, until they are golden brown and tender, about 10 to 12 minutes.
Push the potatoes to the outer edges of the pan and add the ground beef to the center, breaking it apart with a spatula.
Add the diced red onion and bell pepper to the beef as it browns.
Season the entire mixture with sea salt, black pepper, garlic powder, and smoked paprika, then toss everything together once the beef is fully cooked.
Create a small well in the center of the hash and crack the egg into it, cooking until the white is set but the yolk remains runny.
Slide the hash onto a plate and serve immediately while hot.