Whisk eggs, half-and-half, and a pinch of salt together in a small bowl.

Melt butter in a medium nonstick pan over medium-low heat. When butter starts to bubble, pour in egg mixture. Using a silicone spatula, gently swirl the eggs around in circles from the outside in, without stopping, until you start to see small curds, about 20 to 30 seconds.

Switch from making circles to making long sweeps across the pan until you see larger curds, about 20 seconds. When eggs are about 75% cooked, gently fold in cheese. The eggs now should be softly set and still a little runny in places.

Remove the skillet from the heat, and set aside for about 20 to 35 seconds to allow the residual heat to finish cooking to your preferred consistency.