In a bowl, crack the large eggs and whisk them until the yolks and whites are fully combined, introducing some air.

Heat a skillet over medium heat and add the salted butter. Let it melt gently.

Once the butter is bubbling slightly, pour the whisked eggs into the skillet and spread evenly.

Using a spatula, stir the eggs gently in a circular motion until they are just set but still glossy—about 3-4 minutes.

Sprinkle the shredded cheddar cheese over the eggs, folding it in gently to melt.

Remove from heat and garnish with fresh chives, if desired. Serve immediately.