Slice the onion and sweat in a frying pan with a dash of extra-virgin olive oil until golden brown.
In a separate frying pan, fry the potatoes in extra-virgin olive oil together with the sliced garlic.
When they are cooked, but before they turn crispy, take them out of the frying pan to drain off some of the olive oil. Then add them to the other frying pan with the onions and cook over a low heat.
Pour off some of the olive oil used to fry the potatoes and then add the cubed chorizo and fry. When done, add the chorizo to the other frying pan with the onions and potatoes.
Now use the same frying pan to fry the eggs with a spoonful of olive oil, taking care not to cook the yolk. You can then either break the yolk in the frying pan and stir it in with the other ingredients or serve it on top of the potatoes and chorizo on each plate for people to break for themselves.