Shrimp Stir-Fry Soup

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6 ounces snow peas (about 1 1/4 cups), trimmed and sliced on the diagonal

1 tablespoon cornstarch

3 tablespoons low-sodium soy sauce

1 teaspoon toasted sesame oil

3 tablespoons peanut oil or vegetable oil

1 bunch scallions, sliced (white and green parts separated)

4 teaspoons grated peeled ginger

3 carrots, diced

3/4 teaspoon sugar

Kosher salt

3/4 pound shiitake mushrooms, stems removed, caps thinly sliced

6 ounces deli ham (in 1 piece), diced

3 tablespoons rice wine or dry sherry

4 cups low-sodium chicken broth

1 pound medium shrimp, peeled and deveined

1 1/2 cups cooked white rice

Freshly ground white pepper