Dice the Yukon Gold potato into small 1/2-inch cubes to ensure they cook quickly and evenly.
Heat the ghee in a large cast-iron skillet over medium-high heat until shimmering.
Add the diced potatoes to the skillet in a single layer and sear for 5-7 minutes, stirring occasionally, until they develop a golden-brown crust.
Push the potatoes to the outer edges of the skillet and add the ground beef to the center, breaking it apart with a wooden spoon.
Stir in the diced onions and red bell peppers, then season the entire mixture with sea salt, black pepper, garlic powder, and smoked paprika.
Continue to cook for 6-8 minutes until the beef is fully browned and the vegetables have softened.
Use your spoon to create a small well in the center of the hash and carefully crack the egg into it.
Reduce heat to medium, cover the skillet with a lid, and cook for 2-3 minutes until the egg white is set but the yolk remains runny.
Remove from heat, garnish with freshly chopped parsley, and serve immediately directly from the skillet.