First separate the eggs (see How to Separate Eggs and Perfect Eggs in our Online Cookery School techniques video). Yolks into a small bowl and whites into a squeaky-clean large bowl; it helps if you separate the whites into a cup first before adding them to the bowl, then if one breaks, it won't ruin the rest.
Next put the pan on to a low heat to warm through. While that's happening, whisk the egg whites with either an electric hand whisk or a balloon whisk, until they form soft peaks.
Then, using a large metal spoon, quickly fold the egg yolks into the egg whites, adding half of the grated Gruyere and Parmesan and the chives and some seasoning at the same time.
Warm the pan over a low heat and then add the butter to the pan and turn the heat up to high and when the butter is foaming, pile the whole lot into the pan and give it a good hefty shake to even it out.
Now let the omelette cook for 1 minute. Then slide a palette knife round the edges to loosen it, sprinkle the remaining cheese all over the surface and whack the omelette under the pre-heated hot grill, 10 cm from the heat.
Let it cook for 1 more minute, until the cheese has melted and tinged golden.
Next, remove the pan from the heat and let it stand and settle for 2 minutes. Take the pan to the warmed plate, use the palette knife to loosen it all around, then ease one half of the omelette over the other and tilt the whole lot out onto the plate.
Scatter the Parmesan and some snipped chives over the top.
Divide it into two and serve immediately.