01 - Heat olive oil and 1 tablespoon butter in a large nonstick skillet over medium heat until butter melts and pan is evenly coated.
02 - Add diced potatoes to the hot skillet. Cook for 8–10 minutes, stirring occasionally, until golden brown and beginning to soften.
03 - Stir in diced onion and bell pepper. Continue cooking for 4–5 minutes until vegetables are tender and potatoes are cooked through. Season with salt, pepper, and smoked paprika.
04 - Crack eggs into a medium bowl, add milk, and whisk until fully combined and uniform in color.
05 - Push cooked vegetables to one side of the skillet. Add remaining 1 tablespoon butter to the empty side and allow to melt.
06 - Pour egg mixture into the buttered side. Let sit briefly until edges begin to set, then gently scramble with a spatula, gradually incorporating the vegetables as eggs cook.
07 - When eggs reach creamy, just-set consistency, sprinkle shredded cheddar evenly across the entire skillet.
08 - Cover skillet for 1–2 minutes until cheese is fully melted. Gently fold everything together to distribute cheese evenly.
09 - Remove from heat immediately. Garnish with fresh chives if using. Serve hot while cheese remains melted and eggs are creamy.