Heat the oil in a 20cm non-stick fry pan. Add the onion, fry gently for 3 minutes until soft.
Add cubed chorizo (the chorizo will sizzle, releasing spices and oils).
Add the tomatoes and basil, cook for another 1 minute.
Remove from the pan and set aside.
Mix the eggs together with a fork, season.
Return the pan to the heat, when hot, pour in the beaten egg. Swirl the egg mix with the fork for 30 seconds, then scatter in the chorizo mix along with the cheese and parsley.
Place the pan under the grill, until the omelette is golden brown.
To Serve: Add a drizzle of extra virgin olive oil and squeeze of lemon.