Asian Mushroom Soup

2 tablespoons vegetable oil

4 garlic cloves, thinly sliced

1 (2-inch piece) fresh ginger, peeled and thinly sliced

2 quarts reduced-sodium chicken broth

3 tablespoons soy sauce

2 tablespoons fish sauce, optional

2 portobello mushrooms, caps peeled, cleaned and thinly sliced

5-ounces cremini mushrooms, thinly sliced

10 small shiitake mushrooms, cleaned and left whole

Outer leaves of 1 small Napa cabbage or 1/2 large cabbage, leaves roughly torn

2 carrots, peeled, cut in 1/2 lengthwise then in 1/2 crosswise, and very thinly sliced

2 good handfuls snow peas

1 small bunch scallions, thinly sliced

Dark sesame oil