01 - Heat olive oil and 1 tablespoon butter in a large nonstick skillet over medium heat until butter melts and mixture shimmers.
02 - Add diced potatoes to the 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 - Whisk together eggs and milk in a medium bowl until fully combined and slightly frothy.
05 - Push 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 for 30 seconds, 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 across the skillet.
08 - Cover skillet for 1–2 minutes until cheese melts completely. Gently fold everything together to distribute ingredients evenly.
09 - Remove from heat immediately. Garnish with fresh chives if desired and serve while hot.