In a medium bowl, whisk the egg yolks with a generous pinch of sea salt and a few turns of freshly cracked black pepper until smooth, silky, and beautifully blended.
In a separate large bowl, whisk the egg whites—by hand, with an electric mixer, or in a stand mixer—until they form firm, glossy peaks that hold their shape with confidence.
Fold half of the whipped whites into the yolks, stirring gently until the mixture becomes lighter, looser, and beautifully airy. Stir through half of the grated Gruyère or mature Cheddar, along with the minced chives, if using.
Using a silicone spatula, carefully fold in the remaining egg whites with long, deliberate strokes, just until no streaks remain. The mixture should feel feather-light, voluminous, and full of promise.
Warm a 23–25cm non-stick skillet over medium heat and melt the butter until softly foaming. Spoon the soufflé mixture into the pan, gently easing it into an even round and smoothing the surface with your spatula.
Cover the pan and cook for several quiet minutes, until the underside turns delicately golden and the top is only just set—still ever so slightly soft at the centre, if that’s how you like it.
Scatter over the remaining cheese, cover once more, and cook for another minute, just long enough for the cheese to melt into silky perfection.
Carefully slide the omelette onto a warm serving plate, folding it gently over itself into a cloud-soft crescent. Serve immediately, while still impossibly light, warm, and wonderfully indulgent.
