Char the onion and ginger over an open flame or in a dry pan until fragrant and slightly blackened.
In a large pot, combine chicken broth, charred onion, ginger, star anise, and cinnamon stick; bring to a gentle simmer for 15 minutes.
Add the chicken breast to the simmering broth and poach until cooked through, approximately 10-12 minutes.
While chicken cooks, prepare the rice noodles according to package instructions, then drain and set aside.
Remove the chicken from the broth, shred it into bite-sized pieces, and strain the broth to remove the solids.
Stir the fish sauce, sea salt, and black pepper into the strained broth.
Divide the noodles and shredded chicken into a large bowl, pour the hot broth over them, and top with bean sprouts, cilantro, and basil.
Serve immediately with a fresh lime wedge for a bright finish.