Step 1

Whisk eggs, salt, and pepper in bowl until eggs are thoroughly combined and mixture is pure yellow. Spray 10-inch nonstick skillet with vegetable oil spray.

Step 2

Melt butter in skillet over medium-high heat, swirling to coat skillet bottom. When foaming subsides, add egg mixture and cook, gently stirring and scraping bottom of skillet with rubber spatula in circular motion until large curds begin to form and bare spots are visible on bottom of skillet, about 20 seconds.

Step 3

Tilt skillet so uncooked eggs fill bare spots. Run spatula around edge of skillet and push cooked eggs down off sides. Let cook, undisturbed, until bottom of omelet is just set but top is still slightly wet, about 30 seconds.

Step 4

Remove skillet from heat. Sprinkle cheddar over half of omelet. Cover and let sit until cheese has melted, about 1 minute. Fold unfilled half of omelet over filled half to create half-moon shape. Holding plate in 1 hand, tilt skillet to slide omelet onto plate. Serve.