01 - Heat 1 tablespoon olive oil in a large cast-iron skillet over medium heat. Add the diced potatoes and sauté for 6–8 minutes, stirring occasionally, until they begin to soften and develop a golden crust.
02 - Add the remaining olive oil, diced onion, and red bell pepper to the skillet. Continue cooking for 4–5 minutes, stirring occasionally, until the vegetables are softened and fragrant.
03 - Stir in the sliced Cajun beef sausage. Cook for 5–6 minutes, allowing the sausage to brown slightly and the flavors to meld together with the vegetables.
04 - Sprinkle the Cajun seasoning, smoked paprika, salt, and pepper evenly over the mixture. Toss well to combine and ensure all ingredients are coated with the spices.
05 - Create small wells in the hash for each egg. Crack the eggs into the wells, cover the skillet, and cook for 4–6 minutes until the whites are set but yolks remain runny. Alternatively, push the hash to the sides, melt the butter in the center if using, and fry the eggs sunny-side up.
06 - Remove the skillet from heat immediately. Garnish with sliced green onions and serve hot while the eggs are at their desired doneness.