Step 1: Dice the russet potatoes into ½-inch cubes. Place them in a pot of salted boiling water and cook for 5 to 7 minutes until just fork-tender. Drain well and pat dry with a clean kitchen towel.
Step 2: Heat 2 tablespoons of butter in a large cast iron skillet over medium-high heat. Add the diced onion and bell pepper. Cook for 3 to 4 minutes until softened and lightly golden. Add the minced garlic and stir for 30 seconds until fragrant.
Step 3: Add the parboiled potatoes to the skillet and spread them into a single even layer. Let them cook undisturbed for 4 to 5 minutes until a golden crust forms on the bottom.
Step 4: Add the chopped corned beef, smoked paprika, Worcestershire sauce, and black pepper. Stir everything together, then press the mixture flat into the skillet. Cook without stirring for another 4 to 5 minutes to develop a crispy crust. Taste and adjust salt if needed.
Step 5: Use the back of a spoon to create 4 small wells in the hash. Crack one egg into each well. Reduce the heat to medium-low and cover the skillet with a lid. Cook for 3 to 5 minutes until the egg whites are fully set and the yolks are still runny.
Step 6: Remove from heat. Garnish with freshly chopped parsley or chives. Serve immediately with hot sauce and buttered toast on the side.