Add a couple dashes of sesame oil to a large pot over medium heat.
Add the carrots, onion, ginger, and smashed garlic. Sauté for a few minutes until fragrant.
Pour in the chicken stock, beef stock, water, and soy sauce.
Bring to a boil, then lower the heat and let simmer for 1 hour.
Strain the broth, removing the cooked vegetables, ginger, and garlic.
Ladle into bowls and garnish with sliced mushrooms and green onions.
