Combine the chicken broth, sliced ginger, star anise, and cinnamon stick in a large pot. Bring the mixture to a boil over medium-high heat, then reduce to a simmer for 10 minutes.
While the broth simmers, cook the rice vermicelli noodles in a separate pot according to package directions. Drain and set aside.
Remove the ginger slices, star anise, and cinnamon stick from the broth with a strainer. Stir in the fish sauce and shredded rotisserie chicken. Heat the broth for 2 minutes until the chicken is warmed through.
Divide the cooked noodles evenly among four bowls. Ladle the hot broth and chicken over the noodles.
Top each bowl with sliced green onions, bean sprouts, and cilantro leaves. Serve with lime wedges on the side.