It is easier to make one omelette at a time – unless you have two smallish nonstick frying pans. Separate the white and yolk of two of the eggs into two bowls. Beat the egg yolks with half the chives and season with salt and pepper. Divide the chopped cheese into four portions and stir one of the portions into the egg yolks.
Whisk the egg whites with an electric hand whisk until they form still peaks, then gently fold into the cheesy egg mix with a metal spoon. Preheat the grill to hot.
Heat 1 teaspoon of the oil in a non-stick frying pan and add the egg mix. Cook until the omelette is just starting to turn golden underneath, then scatter with another portion of cheese.
Pop the pan under the grill and continue cooking until the cheese has melted and the omelette is puffed and only just set.
Carefully tip the omelette onto a serving plate, folding it in half as you do so. Repeat with the remaining two eggs to make the second omelette. Serve with roasted vegetables, if using.