Crack the eggs into a mixing bowl, add a splash of milk or cream, and season with salt and pepper. Whisk vigorously until the mixture is smooth, slightly frothy, and well combined.
Grate or chop your cheese into small, meltable pieces and set aside.
Place a non-stick skillet over medium-low heat and add the butter. Let it melt gently, until it bubbles softly and turns a light golden hue—this aroma signals the pan is ready.
Pour the beaten eggs into the skillet, tilting the pan to spread them evenly. Let them cook undisturbed for about 30 seconds until the edges begin to set and you hear a gentle crackling sound.
Using a spatula, gently push the cooked edges toward the center while tilting the pan to allow raw eggs to flow outward. Continue this process for about a minute until the surface is mostly set but still slightly moist and silky.
Sprinkle the cheese evenly over one half of the eggs. Cover the skillet briefly, about 20 seconds, until the cheese begins to melt and the eggs are just cooked through but still tender inside.
Carefully fold the omelette in half using your spatula, creating a neat half-moon shape. Let it cook for another 10 seconds to ensure the cheese is gooey inside.
Gently slide the omelette onto a plate, letting it rest for 30 seconds. This helps settle the cheese and eggs, finishing the melt and softening the exterior slightly.
Sprinkle with chopped herbs if desired, and serve immediately while the cheese inside is warm and gooey. Enjoy the tender, golden exterior and rich, melty core.
