Heat dry heavy skillet over medium-high. Char cut sides of onion and ginger 6 to 8 minutes until dark patches form. Add star anise, cinnamon, cloves, and coriander in final 1 minute, stirring spices.
Transfer aromatics and spices to large pot with broth, water, and chicken. Gently simmer 30 to 35 minutes until chicken 165°F.
Remove chicken; fine-strain broth, discarding aromatics. Return broth to pot; add fish sauce and sugar.
Cook noodles separately per package; drain and briefly rinse with warm water. Pull chicken from bones and shred; discard bones.
Add sprouts to simmering broth 1 minute. Stir in lime juice; divide noodles and chicken among six bowls.
Ladle hot broth and sprouts over noodles; scatter scallions evenly.