01 - Heat olive oil and 1 tablespoon butter in a large nonstick skillet over medium heat until butter melts and coats the pan.
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. Cook for 4–5 minutes until vegetables are soft 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 uniform in color.
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 into the buttered area. Let set briefly, then gently scramble with a spatula, gradually incorporating the vegetables as eggs cook.
07 - When eggs are just set but still creamy, sprinkle shredded cheddar cheese evenly over the entire scramble.
08 - Cover skillet for 1–2 minutes until cheese melts completely. Uncover and gently fold everything together until well combined.
09 - Remove from heat immediately. Garnish with fresh chives if desired and serve hot while cheese is still melted.