01 - Heat butter or oil in a large nonstick skillet over medium heat until shimmering.
02 - Add diced potatoes to the hot skillet. Cook, stirring frequently, until golden brown and tender, about 10-12 minutes.
03 - Add diced onion and bell pepper. Sauté for 3-4 minutes until softened and fragrant.
04 - While vegetables cook, whisk together eggs, milk, salt, pepper, and smoked paprika in a mixing bowl until fully combined.
05 - Reduce heat to medium-low. Pour egg mixture evenly over the vegetables. Let sit undisturbed for 30 seconds to begin setting.
06 - Gently fold and stir with a spatula as the eggs set. Continue cooking until mostly set but still slightly creamy, about 2-3 minutes.
07 - Sprinkle shredded cheddar cheese evenly over the eggs. Let sit for 1 minute, then gently fold to incorporate as the cheese melts.
08 - Slide the scramble onto plates and garnish with chives or green onions. Serve immediately while hot.