To make Italian onion soup, set a frying pan over medium-high heat, and add 2 tablespoons of extra-virgin olive oil. Finely chop 1 tablespoon of garlic, and cook it in the oil until it just starts to brown. Thinly slice 8 cups of onions, and add them to the garlic with 1/4 teaspoon of sea salt or gray salt. Cook the onions until they begin to soften, about seven minutes.
Set the stovetop heat to medium, and cook the onions and garlic for an additional 10 minutes, until the onions turn golden brown. Finely chop 1 tablespoon of fresh sage leaves, and add them with 1/4 cup of balsamic vinegar to the onions and garlic. Heat and stir the ingredients until the liquid evaporates, about two to four minutes. Mix in 1 32-ounce carton of beef broth, and allow the ingredients to simmer together for 10 minutes.
Set the oven to broil. Cut 4 pieces of Italian country bread in 3/4-inch thick slices. Shred 1 cup of mozzarella cheese, and top the bread slices with it. Transfer the bread to a flat baking pan, and broil them until the cheese melts, approximately four to six minutes. Ladle the onion soup into four bowls, and top each bowl with a slice of the bread to serve.