Melt half of the butter in a frying pan then add the tomato and oregano, cooking it for 2-3 minutes. Remove to a plate and wipe the frying pan clean.
Whisk the eggs together, melt the remaining butter in the frying pan then add the eggs.
Cook on a low heat, using a spatula to lift the sides up and allow the raw egg to escape out the sides (this gives you a fluffier omelette).
After 2 minutes place the tomato and cheese across half of the omelette. Cook for a further minute then remove from the heat. Flip the free half of the omelette over the tomato and cheese half.
Cut into fingers for baby to serve themselves.