Heat 1 tablespoon of the oil in a large frying pan (with about a 23cm base). Tip in the chorizo and fry for 4-5 minutes until crisp. Remove with a slotted spoon and drain on kitchen towel. Pour the chorizo fat into a heatproof bowl and wipe out the pan.
Put the remaining 1 tablespoon of olive oil and 2 tsp of the chorizo fat into the pan. Add the shallots and fry for a couple of minutes, then drop the potato chunks in the pan and cook over a medium heat, stirring occasionally, for about 6-7 minutes or until both are turning brown. Cover the pan with a lid and continue to cook on a low heat for a further 4-5 minutes, or until the potatoes are tender but still holding their shape.
Beat the eggs in a bowl, season with pepper and stir in the parsley. Return the chorizo to the pan with the potato, then pour in the eggs. Gently and briefly stir to combine, then leave to cook over a medium heat for 4-5 minutes or until starting to set and the bottom of the omelette is golden. Tip the pan occasionally so the raw egg can run to the edges of the pan to cook. Preheat the grill to high.
Put the pan under the grill for a couple of minutes to finish cooking the top of the omelette. Slide the omelette onto a board or flat serving plate, scatter with extra parsley and cut into thin wedges to serve.
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