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 they begin to soften and develop a golden crust.
02 - Add remaining olive oil, diced onion, and red bell pepper to the skillet. Cook for 4–5 minutes until vegetables are softened and fragrant.
03 - Stir in sliced Cajun beef sausage. Cook for 5–6 minutes, allowing sausage to brown and render its fat while flavors meld together.
04 - Sprinkle Cajun seasoning, smoked paprika, salt, and pepper evenly over the mixture. Toss thoroughly to combine and coat all ingredients.
05 - Push hash to skillet sides, melt butter in center if using, and crack eggs into the well. Cover and cook 4–6 minutes for sunny-side up, or flip for over-easy doneness.
06 - Remove from heat immediately. Garnish generously with sliced green onions and serve hot while eggs are perfectly cooked.