Dice the chorizo and pepper. Finely chop the onion.
Heat a frying pan and add the chorizo and pepper. Gently cook until the chorizo releases its fat and the pepper gets soft. Transfer these to a plate.
Whisk the eggs with the milk.
Melt the butter in the pan, then pour in the egg mixture, allowing it to spread out. After a minute or so, when the egg is jelly-like, scatter the chorizo and pepper mixture on top, then the onion and finally the cheese. Put the lid on, turn down the heat and cook for about 5 minutes until the egg has just set and the cheese has melted.
Scatter the parsley on to and fold the omelette in half. Cook for another minute then slide it onto a plate. Cut it into half and serve.