01 - Heat 1 tablespoon olive oil in a large skillet (preferably cast-iron) over medium heat. Add the diced potatoes. Sauté for 6–8 minutes, stirring occasionally, until they begin to soften and turn golden.
02 - Add the remaining olive oil, diced onion, and red bell pepper to the skillet. Cook for another 4–5 minutes, until the vegetables are softened.
03 - Stir in the sliced Cajun beef sausage. Cook for 5–6 minutes, allowing the sausage to brown and the flavors to meld.
04 - Sprinkle the Cajun seasoning, smoked paprika, salt, and pepper over the mixture. Toss well to combine.
05 - Push the hash to the sides of the skillet, melt butter in the center if desired, and crack the eggs into the well. Cover and cook 4–6 minutes for sunny-side up eggs, or flip for over-easy. Alternatively, make small wells in the hash for each egg, then crack the eggs into them.
06 - Remove from heat. Garnish with sliced green onions. Serve hot.