Chicken Soba Noodle Soup

Name: Chicken Soba Noodle Soup
Ingredients: 1 pound small skinless, boneless chicken thighs; 6 cups low-sodium chicken broth; 6 slices fresh ginger, lightly smashed, plus 1 tablespoon finely grated; 2 scallions, whites cut into 2-inch pieces and greens thinly sliced; Kosher salt and freshly ground pepper; 1 cup sugar snap peas; 3 carrots; 1 9.5-ounce package soba; 4 ounces sliced shiitake mushrooms; 1/4 cup low-sodium soy sauce; 2 tablespoons fresh lemon juice; Shichimi togarashi (Japanese seasoning) or Asian chili sauce, for topping