Fry the chorizo and peppers in olive oil in a hot pan for 4 minutes.
Whisk the eggs until light and frothy then add a dash of milk, some salt and pepper and half the chives.
Add the egg to the hot pan with the pepper and chorizo and cook for two minutes.
Slice the mozzarella and place over one half the omelette. Fold the other half over to cover the cheese and cook for 1-2 minutes, flipping to make sure both sides are cooked.
Grate some cheddar over the top and place under a hot grill for 30 seconds to a minute.
Scatter over the rest of the chives and serve.
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