Lightly whisk the eggs in a small bowl.
Heat a little olive oil in a non-stick frying pan. Add the egg mixture, letting it spread out evenly.
Put the anchovy and tomato pieces on one half of the omelette, letting them sink into it a bit. Cook for a couple of minutes, then add the cheese. Cook for another 2 minutes until the cheese has melted and the egg is set. Scatter the basil leaves on top.
Carefully fold the omelette in half (the empty half on top of the layered half). Cook for a few seconds, then slide it to a plate and serve with a crispy salad on the side.