Slice two heads of garlic in half crosswise; set aside. Separate cloves from the remaining head, peel and crush lightly.
Heat the olive oil in a large saucepan over medium heat. Add the crushed garlic cloves and cook, stirring often, until golden brown and softened, 8-10 minutes.
Add 8 cups of water and increase the heat to high, and bring the mixture to a boil. Add the herbs and reserved halved heads of garlic. Reduce heat so the broth is at an active simmer and cook until garlic is very tender and the broth is reduced by nearly half, 35-45 minutes. Season generously with sea salt and freshly cracked pepper, to taste.
Strain broth through a mesh sieve into a large bowl. Divide broth among bowls. Side Note: Sip it as is, or you can add cooked noodles or drizzle in some whisked eggs to make an egg drop soup.
Do Ahead: Broth can be made 3 days ahead. Let cool; seal in an airtight container and store in the refrigerator.