01 - Heat butter or oil in a large nonstick skillet over medium heat until shimmering.
02 - Add diced potatoes to the skillet. Cook, stirring frequently, until golden brown and tender, about 10-12 minutes.
03 - Add onion and bell pepper (if using). 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 stir and fold with a spatula as the eggs set. Continue cooking until mostly set but still slightly creamy, about 2-3 minutes.
07 - Sprinkle shredded cheddar evenly over the eggs. Let sit for 1 minute, then gently fold to incorporate as the cheese melts.
08 - Slide onto plates and garnish with chopped chives or green onions if desired. Serve immediately while hot.