Bring the water to a boil in a 3- or 4-quart saucepan or soup pot. Add the minced or pressed garlic, 1-½ teaspoons salt, bay leaf, and thyme or sage. Reduce the heat, cover and simmer 15 minutes. Taste: Does it taste good? Is there enough salt? Garlic?
Toast the bread. As soon as it’s done, rub both sides with the cut clove of garlic and set aside.
Beat together the eggs and optional olive oil. Spoon a ladleful of the hot soup into the eggs and stir together. Then turn off the heat under the soup, and stir in the egg mixture. The eggs should cloud the soup but they shouldn't scramble if the soup isn't boiling. Stir in the pepper and parsley.
Place a garlic crouton in each bowl. Ladle in the soup, sprinkle Parmesan or Gruyère over the top, and serve.
