Fish and Vegetable Soup with Lime, Ginger, and Cilantro

4 garlic cloves

1 tablespoon chopped peeled fresh ginger

1 jalapeño chili, seeded, quartered

2 tablespoons vegetable oil

4 cups fish stock or bottle clam juice

2 cups water

6 tablespoons fresh lime juice

3 tablespoons minced fresh lemongrass or 1 tablespoon grated lemon peel

2 whole star anise*

1 cup grated peeled carrots

1 cup mung bean sprouts

2 ounces fresh shiitake mushrooms, stemmed, caps sliced (about 1 1/4 cups)

1/2 cup chopped tomatoes

6 green onions, cut diagonally into 1-inch lengths

1 1/2 pounds assorted fish fillets (such as snapper, orange roughy, and sea bass), cut into 2x1-inch strips

1/2 cup cilantro leaves