Pour the water into a large saucepan and bring to a boil. Add the crushed pink garlic and the egg white. Add salt and pepper and mix. Cook for 3 minutes. Add the vermicelli and cook for 3 minutes more. Prepare a mayonnaise with the egg yolk, pepper, salt, mustard and oil. (You may not need to use all the oil). Dilute it with a ladle of warm stock and incorporate it delicately into your soup.