Pour the water and the broth into a deep pot with the salt.
Peel and crush 10 of the garlic cloves (I used the base of my glass measuring cup), then put into the broth.
Add the bay leaves and the 1st teaspoon of olive oil. Cook for 15 minutes over medium-high heat.
Cut the chicken into pieces, and stir into the soup along with all of the herbs (except the parsley). Peel and finely dice the last garlic clove, and add to the pot. Cook about 10 more minutes until the chicken is cooked through.
In the meantime, brush both sides of the bread slices with olive oil, and then fry over medium heat until golden brown. (Or you can bake them, I suppose!).
Set the toast to the side, and fry each egg one at a time. Sprinkle with parsley and ground black pepper. Set these to the side too.
Bring the soup to a boil for 5 minutes, and then strain the soup into a bowl, and then return the broth to the pot.
Rinse any clinging herbs from the chicken pieces, and put the chicken back into the soup.
Discard all other solids.
To serve, place 2 slices toast into the bottom of each (wide and shallow) bowl. Sprinkle 2 tablespoons of Parmesan cheese over each bowl. Ladle the soup over the bread and cheese, and top with an egg. Sprinkle with parsley and serve hot. (Eat this right away, or the bread will become soggy).
Serve with fresh apple slices and lightly steamed broccoli or asparagus tips.