Chilled Soba with Tofu and Sugar Snap Peas

Name: Chilled Soba with Tofu and Sugar Snap Peas
Ingredients: 1 large dried shiitake mushroom; 2 1/2 cups water; 8 (1-inch) pieces kombu (dried kelp); 1/2 cup soy sauce (preferably Japanese); 1/4 cup mirin (Japanese sweet rice wine); 3 tablespoons ponzu sauce (not containing dashi); 1 tablespoon sugar; 1 tablespoon Asian sesame oil; 1 pound sugar snap peas, thinly sliced; 10 ounces baby spinach (16 cups); 1 pound dried soba noodles; 1 (14- to 18-ounce) package silken tofu; 1 cup thinly sliced scallions, divided; 2 tablespoons thin matchsticks of peeled ginger