Cook the spaghetti in 3-4 l boiling salted water (1 teaspoon salt per litre) according to the instructions on the packet. Peel the skin from the chorizo, cut the sausage into slices. Grate parmesan finely. Whisk eggs, cream and 2⁄3 Parmesan in a large bowl, season with salt and pepper.
Wash parsley, shake dry, pluck off the leaves and cut into fine strips.
Heat the oil in a large frying pan. Sauté the chorizo in it vigorously while turning. Drain the spaghetti and add to the chorizo. Mix with the sausage and fry briefly.
Remove the pan from the heat and mix the pasta mixture in the bowl with the egg-cream mixture. Season the carbonara with salt and pepper, arrange and sprinkle with parsley. Add the rest of the parmesan.