01 - Heat 1 tablespoon olive oil in a large cast-iron skillet over medium heat. Add diced potatoes and sauté for 6 to 8 minutes, stirring occasionally, until edges begin to golden and potatoes start to soften.
02 - Add remaining olive oil, diced onion, and red bell pepper to the skillet. Cook for 4 to 5 minutes, stirring frequently, until vegetables are softened and fragrant.
03 - Stir in sliced Cajun beef sausage. Cook for 5 to 6 minutes, allowing sausage to develop a rich brown color and release spicy oils into the vegetable mixture.
04 - Sprinkle Cajun seasoning, smoked paprika, salt, and pepper evenly over the skillet. Toss thoroughly to ensure spices coat all ingredients evenly. Adjust seasoning to taste.
05 - Create four small wells in the hash mixture. Crack an egg into each well. Alternatively, push hash to skillet edges, melt butter in center if using, and crack eggs into the cleared space. Cover skillet and cook for 4 to 6 minutes until whites are set but yolks remain runny, or cook longer for firmer yolks.
06 - Remove skillet from heat immediately. Scatter sliced green onions over the top as garnish. Serve piping hot directly from the skillet.