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 skillet and cook for 8–10 minutes, stirring occasionally, until golden brown and beginning to soften.
03 - Stir in 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 - While vegetables cook, whisk together eggs and milk in a medium bowl 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 let it melt.
06 - Pour egg mixture over melted butter. Let set briefly, then gently scramble with a spatula, gradually incorporating vegetables as eggs cook.
07 - When eggs are just set but still creamy, sprinkle shredded cheddar evenly over the entire mixture.
08 - Cover skillet for 1–2 minutes until cheese melts completely. Gently fold everything together, remove from heat, and garnish with chives if desired.