Heat the oil in a large frying pan, add the tomatoes, in batches if necessary, and cook, stirring gently, for 2–3 minutes until softened. Add the basil and season with salt and pepper. Transfer to a bowl and keep warm in a moderate oven.
Beat the eggs, mustard and salt and pepper together in a separate bowl. Melt a quarter of the butter in an omelette pan or small frying pan. As soon as it stops foaming, swirl in a quarter of the egg mixture and cook over a medium heat, forking over the omelette so that it cooks evenly.
Dot a quarter of the goats' cheese over one half of the omelette as soon as it is set on the underside, but still a little runny in the centre, and cook for a further 30 seconds. Carefully slide the omelette on to a warmed serving plate, folding it in half as you go. Keep warm in the oven. Repeat with the remaining egg mixture to make 3 more omelettes.
Garnish the omelettes with watercress and serve with the tomatoes and a green salad.