Crack the eggs into a mixing bowl and whisk vigorously until fully blended and frothy.
Add the milk (or cream) and whisk again to combine.
Heat a non-stick skillet over low to medium-low heat and add the butter. Let it melt completely but avoid browning.
Pour the egg mixture into the skillet. Let it sit undisturbed for a few seconds until the edges begin to set.
Using a spatula, gently push the eggs from the edges toward the center, folding and stirring continuously.
Cook slowly, stirring constantly, until the eggs are just set but still slightly soft and creamy.
Remove the skillet from the heat immediately, as the residual heat will finish cooking the eggs.
Season with salt and freshly ground black pepper to taste.
Serve immediately, garnished with chopped chives or parsley if desired.