In the Bordeaux area onion soup includes garlic. Also, it is a cream of onion soup and therefore differs strikingly from the bouillon-like onion soup of Paris.
Put bacon fat into a large saucepan. Add onions and garlic. Stir-cook until transparent and soft. Do not let mixture brown. Stir in flour. Cook 1 minute or so. Add broth and water. Stir until it comes to a boil. Season with salt and pepper. Cover and simmer 30 minutes with lid set ajar.
Beat together yolks, crème, and lemon juice. Remove soup from heat. Gradu