Vietnamese Chicken Noodle Soup

Name: Vietnamese Chicken Noodle Soup
Ingredients: 1 3½–4-lb. chicken; 1 large onion, peeled, halved through root; 2 medium carrots, peeled, cut into 1” pieces; 1 celery stalk, cut into 1” pieces; 2 pounds skin-on, bone-in chicken legs (thigh and drumstick; about 4); ¼ teaspoon Chinese five-spice powder; 1 teaspoon grated peeled ginger, plus one 4” piece ginger, peeled, halved lengthwise; 1 tablespoon kosher salt, plus more; 1 tablespoon sugar, plus more; 2 medium onions, peeled, halved through root; 2 6” pieces lemongrass, tough outer layer removed, stalk lightly smashed; 6 black cardamom pods, crushed; 4 whole star anise pods; 2 cinnamon sticks; 6 whole cloves; 1 tablespoon fish sauce (such as nam pla or nuoc nam); 1 pound dried wide rice noodles; 8 oz. mung bean sprouts (about 2 cups); Spicy Pickled Shallots (click for recipe), fresh tender herbs (such as Thai basil, mint, or cilantro), and lime wedges (for serving)