Char the white onion and fresh ginger over an open gas flame or under a high broiler until the skins are blackened and fragrant.
In a large stockpot, lightly toast the star anise and cinnamon stick over medium heat for 1-2 minutes until their oils are released.
Add the beef bone broth, charred onion, and charred ginger to the pot; bring to a boil, then reduce heat and simmer for 20 minutes.
While the broth simmers, prepare the rice noodles according to the package instructions, then drain and set aside.
Strain the broth through a fine-mesh sieve into a clean pot, discarding the solids, and stir in the fish sauce, sea salt, and black pepper.
Place the cooked rice noodles in a large serving bowl and arrange the raw, thinly sliced beef eye of round on top.
Pour the boiling hot broth directly over the beef slices, which will cook them instantly to a tender medium-rare.
Top the bowl with fresh bean sprouts, Thai basil, and cilantro, serving with a fresh lime wedge on the side.