Whisk the Eggs Thoroughly: Crack the eggs into a small mixing bowl. Use a wire whisk to beat them vigorously for a full minute until the mixture is pale and slightly frothy. This step is key to incorporating air for a fluffy finish.
Melt Butter Slowly: Place a 7-inch nonstick skillet over low heat. Add the butter and let it melt gradually until it starts to foam slightly—this ensures a gentle, even cooking surface.
Add the Eggs Off-Heat: Remove the pan briefly from the heat. Pour the beaten eggs into the pan. Give the top of the mixture another light whisk, keeping the whisk near the surface without scraping the pan bottom.
Return to Heat and Whisk: Set the skillet back over low heat. Continue whisking softly as the eggs begin to foam at the top. Once foam is visible, sprinkle in the shredded cheddar and lightly whisk again to incorporate the cheese.
Begin Gentle Folds: Allow the eggs to sit undisturbed for about 5–7 seconds. Then, using a silicone spatula, gently push the set edges of the eggs toward the center, tilting the pan so raw egg flows into the cleared space.
Rotate and Fold: Repeat this motion—pushing set egg inward and tilting—until most of the eggs have formed soft, fluffy curds and only a little moisture remains.
Finish with Residual Heat: Remove the skillet from the heat. Let the remaining warmth finish cooking the eggs. Lightly fold the eggs a few more times so that any wet spots are evenly set.
Serve and Season: Gently divide the eggs into smaller portions with the spatula to resemble traditional scrambles. Season with salt and freshly ground pepper, garnish with chives (if using), and serve right away.