01 - Heat butter or oil in a large nonstick skillet over medium heat until shimmering.
02 - Add diced potatoes to the skillet and cook, stirring frequently, until golden brown and tender, about 10-12 minutes.
03 - Add diced onion and bell pepper (if using) to the potatoes. 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 the egg mixture evenly over the vegetables in the skillet. Let sit undisturbed for 30 seconds to begin setting.
06 - Gently stir and fold with a spatula as the eggs begin to 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 until melted, then gently fold to distribute the cheese throughout.
08 - Slide the scramble onto plates and garnish with chopped chives or green onions if desired. Serve immediately while hot.