Bring 3-4 l salted water (approx. 1 teaspoon salt per litre) to the boil. Peel onion and garlic, dice onion. Chop garlic, sprinkle with salt and crush with a knife blade.
Peel the skin from the chorizo, cut the sausage into slices. Put the pasta in boiling water, cook according to the instructions on the packet. Stir from time to time so they don't stick together.
Heat the oil in a frying pan. Sauté the onion and garlic in it. Add the slices of chorizo and fry for 2-3 minutes, turning.
Wash and chop the parsley. Grate the parmesan. Whisk eggs and cream. Stir in parmesan and parsley. Season with salt and pepper. Fold in the chorizo-onion mixture.
Shortly before the end of the cooking time take a noodle out of the pot and try it. Or cut it up and check if the core is still a little visible. Then the pasta is cooked, but still has bite.
Drain the pasta and put it back into the pot. Add the egg mixture to the hot noodles in the pot and immediately mix everything well. Season with pepper and serve.