Braised Egg Tofu with Shiitake Mushrooms

Name: Braised Egg Tofu with Shiitake Mushrooms
Ingredients: 12 medium dried shiitake mushrooms (about 1 1/2 cups); One 2-inch piece kombu; 1/3 cup plus 1 tablespoon cornstarch; 1/4 cup canola or vegetable oil; Two 8.6-ounce tubes egg tofu, cut crosswise into 1/2-inch-thick rounds (see Cook’s Note); 3 cloves garlic, minced; 2 thinly sliced ginger coins; 1 scallion, minced, white and green parts separated; 1 medium carrot, peeled and cut 1/4 inch thick on a bias; 2 tablespoons vegetarian mushroom oyster sauce; 1 teaspoon low-sodium soy sauce; 1/2 teaspoon dark soy sauce; Kosher salt; 4 ounces snow peas (about 1 1/2 cups), trimmed; 2 medium baby bok choy (about 8 ounces), leaves separated; 3 cups cooked white rice, for serving