Crack the eggs into a small bowl and whisk vigorously until the yolks and whites are fully combined and slightly frothy, about 15 seconds.
Heat the non-stick skillet over medium-low heat and add the butter, letting it melt and foam, filling the pan with a rich aroma.
Pour the whisked eggs into the skillet, tilting it gently to spread the eggs evenly across the surface, creating a thin, even layer. Let cook for about 10-15 seconds until the edges begin to set.
Use the spatula to gently push the eggs from the edges toward the center, allowing the uncooked eggs to flow to the edges. Continue this process until the eggs are mostly cooked but still slightly runny on top, about 30 seconds.
Sprinkle the shredded cheese evenly over one half of the omelette, making sure it covers the surface completely to melt into that gooey layer.
Allow the cheese to melt for about 30 seconds, watching as it becomes gooey and begins to bubble slightly, filling the air with a savory scent.
Gently fold the omelette in half over the cheese using the spatula, pressing lightly to seal the edges and encourage the cheese to stay inside.
Cook for another 15-20 seconds, allowing the inside to finish setting and the cheese to fully melt into a luscious, gooey center.
Gently slide the omelette onto a plate, letting it rest for about a minute to let the filling set and prevent cheese from oozing out when sliced.
Slice the omelette in half or into wedges, revealing the golden exterior and the melty, cheesy interior. Serve immediately and enjoy the rich, fluffy texture.
