Onions peel, halve and in fine strips cut. Wash the tomatoes, drain and cut in half. Cut the chorizo into slices. Put oil in 2 frying pans and heat.
Add half onions and half chorizo and sauté for about 2 minutes, turning vigorously. Add tomatoes and beat 2 eggs in each pan. Fry over medium heat for about 4 minutes.
Wash basil, shake dry, pluck leaves from the stalks and chop coarsely. Season eggs with salt and pepper. Arrange pans and sprinkle with basil.