Heat oil in an oven proof frying pan and add your sliced potatoes and fry for a 3-4 minutes. Then add your sliced Chorizo and fry, stirring occasionally until the red oils begin to seep out into the pan.
Add your sliced red peppers and stir. Pre-heat your grill to a medium heat.
In a separate bowl, whisk up your eggs with a little seasoning. Pour the eggs into the frying pan and stir quickly and well in order to coat all the other ingredients and distribute evenly over the whole pan.
Leave the cook from the underneath for 4-5 minutes. Then top with grated cheese and transfer to under the grill to set the top of the omelette and melt the cheese, another 4-5 minutes. Serve straight from the pan.