Yaki Udon

Name: Yaki Udon
Ingredients: 18 to 20 ounces fresh or frozen udon noodles; 1/4 cup mushroom broth; 2 tablespoons sake; 2 tablespoons soy sauce; 1 1/2 teaspoons sugar; Kosher salt and freshly ground pepper; 8 ounces skinless, boneless chicken breasts, sliced 1/4 inch thick; 2 tablespoons vegetable oil; 1/4 small head napa cabbage, chopped into 1 1/2-inch pieces; 1 carrot, thinly sliced on an angle; 3 scallions (white and green parts separated), thinly sliced; 1 cup snow peas, trimmed; 6 cloves garlic, minced