01 - Heat 1 tablespoon olive oil in a large cast-iron skillet over medium heat. Add diced potatoes and sauté for 6–8 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 4–5 minutes, stirring occasionally, until vegetables are softened and fragrant.
03 - Stir in sliced Cajun beef sausage. Cook for 5–6 minutes, allowing sausage to brown evenly and release its aromatic oils into the vegetable mixture.
04 - Sprinkle Cajun seasoning, smoked paprika, salt, and pepper over the skillet. Toss thoroughly to distribute spices evenly and let flavors meld for 1 minute.
05 - Push hash mixture to the sides, creating wells in the center. Melt butter if using, then crack eggs into the wells. Cover skillet and cook for 4–6 minutes until whites are set but yolks remain runny. Alternatively, flip eggs for over-easy preparation.
06 - Remove skillet from heat immediately. Scatter sliced green onions over the top as garnish. Serve hash directly from the skillet while hot, ensuring each portion receives sausage, vegetables, and an egg.