1. Sauté the burdock, carrots, ginger, and garlic in sesame oil 10 minutes, stirring often. Remove and discard the garlic as soon as it turns slightly brown.
2. Meanwhile, toast sesame seeds in a frying pan over medium heat, stirring constantly, until they pop and become slightly brown and fragrant. Remove the sesame seeds from frying pan and set aside.
3. Add the remaining ingredients to the sautéed vegetables, bring to a boil, reduce the heat, cover, and simmer 15 minutes.
4. Add the sesame seeds.
Serve hot as an appetizer, a condiment, or a side dish.