Preheat your oven to 400°F. Cut the tops off the garlic heads or slice them in half horizontally. Place the garlic halves in a small baking dish.
While the garlic roasts, heat the remaining olive oil in a large pot over medium heat. Add the chopped onion, oregano, and thyme, and sauté for about 5 minutes until it becomes translucent.
Pour in the broth and season with salt and black pepper. Bring the mixture to a simmer and let it cook for about 15-20 minutes, or until the potato is tender.