01 - Heat butter or oil in a large nonstick skillet over medium heat until shimmering.
02 - Add diced potatoes to the hot pan. Cook, stirring frequently, until golden brown and fork-tender, about 10-12 minutes.
03 - Add onion and bell pepper. Sauté for 3-4 minutes until softened and fragrant.
04 - In a mixing bowl, whisk together eggs, milk, salt, pepper, and smoked paprika 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 push and fold eggs with a spatula from the edges toward the center. Cook until mostly set but still slightly creamy, about 2-3 minutes.
07 - Sprinkle cheddar cheese evenly over the eggs. Let sit for 1 minute, then gently fold just until cheese is melted and incorporated.
08 - Transfer to plates immediately. Garnish with chopped chives or green onions if desired. Serve hot.