Make the hollandaise in a food processor: whisk the egg yolks and lemon together. Heat the butter until foaming and, with the food processor on slow, add the butter gradually until the whole thing emulsifies and you get a smooth, creamy sauce. Stir in the tarragon and set aside.

In a bowl, whisk the six eggs together with the Parmesan and season well. Heat the butter in a large non-stick frying pan and fry the tomatoes until almost but not quite soft. Turn up the heat and pour in the eggs. Use a plastic palette knife to gently pull the egg from the side of the pan into the centre and let the liquid go underneath, so you get a nice, fluffy omelette. When the top looks almost but not quite cooked, arrange the lobster and chives on top and fold the omelette in half. Serve with the hollandaise on the side.