In a medium bowl, crack open the large eggs and add a splash of milk, a pinch of salt, and a dash of black pepper. Whisk until frothy, about 1-2 minutes.

Place a non-stick skillet over medium-low heat and add a tablespoon of butter. Allow it to melt, swirling to coat the pan.

Pour the whisked egg mixture into the skillet and let sit for 30 seconds to 1 minute until the edges start to set.

Using a rubber spatula, gently push the edges toward the center, letting the uncooked liquid flow out. Stir intermittently for about 2-3 minutes.

Once soft curds form, sprinkle shredded cheese over the top and fold into the eggs gently. Allow to melt for about 1 minute.

Remove from heat when the eggs are glossy and slightly runny, about 1 minute after adding cheese.