01 - Heat the olive oil and 1 tablespoon butter in a large nonstick skillet over medium heat until butter melts and mixture shimmers.
02 - Add the diced potatoes to the skillet. Cook for 8-10 minutes, stirring occasionally, until golden brown and beginning to soften.
03 - Stir in the diced onion and bell pepper. Continue cooking for 4-5 minutes until vegetables are soft and potatoes are cooked through. Season with salt, pepper, and smoked paprika.
04 - While vegetables cook, whisk together the eggs and milk in a medium bowl until fully combined and uniform in color.
05 - Push the cooked vegetables to one side of the skillet. Add the remaining 1 tablespoon butter to the empty side and let it melt.
06 - Pour the egg mixture into the buttered area. Let set for 30 seconds, then gently scramble with a spatula. Gradually incorporate the vegetables as the eggs begin to firm up.
07 - When eggs are just set but still creamy, sprinkle the shredded cheese evenly over the entire skillet.
08 - Cover the 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. Serve hot while cheese is still melted.