Place a non-stick skillet over medium-high heat and add the unsalted butter.
Once the butter is foaming, add the potato cubes and sauté for 4 minutes, turning occasionally until edges are golden and crispy.
Reduce the heat to medium-low and pour the whisked eggs into the skillet over the potatoes.
Allow the base to set for 20 seconds, then use a spatula to gently fold the mixture, creating large curds.
Evenly distribute the shredded cheddar cheese over the eggs while they are still slightly moist.
Continue to fold gently for 1 minute until the eggs are just set and the cheese is fully melted.
Transfer to a plate, season with salt and pepper, and garnish with minced chives.