Crack the eggs into a small mixing bowl, add a pinch of salt and pepper, and gently whisk until just combined. You want the yolks and whites to be integrated but not overmixed.
Place your non-stick skillet over medium-low heat and add a tablespoon of butter. Let it melt slowly, until it foams softly and releases a warm, nutty aroma, about 30 seconds.
Pour the beaten eggs into the skillet, tilting the pan gently to distribute them evenly in a thin layer. Let the eggs cook undisturbed for about 1-2 minutes, until the edges start to set and turn golden.
Sprinkle the shredded cheese evenly over the surface of the eggs. Wait for the cheese to soften and begin melting, which should take about 30 seconds—look for the cheese to become gooey and slightly bubbling at the edges.
Using your spatula, gently fold one side of the omelette over the cheese, creating a half-moon shape. Be careful to keep the fold gentle to avoid tearing the eggs.
Cook the folded omelette for another 30 seconds to 1 minute, allowing the cheese to melt completely inside and the eggs to finish cooking without becoming rubbery. The surface should be golden with a slight crispness.
Slide the omelette onto a plate, letting it rest for about 30 seconds. This brief pause helps settle the flavors and ensures the cheese is irresistibly gooey in every bite.
Garnish with extra herbs or a dash of hot sauce if desired, then serve immediately while warm and gooey. Enjoy the tender eggs paired with the luscious, melted cheese for a perfect breakfast treat.
