Char the white onion and fresh ginger over an open gas flame or under a broiler until the skins are blackened and fragrant.
In a large pot, toast the star anise and cinnamon stick over medium heat for 2 minutes to release their essential oils.
Add the beef broth, charred onion, ginger, and fish sauce to the pot and bring to a gentle simmer for 20 minutes.
While the broth infuses, cook the rice noodles in a separate pot of boiling water according to package instructions, then drain and set aside.
Thinly slice the beef eye of round against the grain into paper-thin pieces using a very sharp knife.
Strain the broth through a fine-mesh sieve to remove the solids, then return the clear liquid to the pot and bring it to a rolling boil.
Place the cooked noodles in a large bowl and layer the raw beef slices on top.
Pour the boiling broth over the beef to cook it instantly, then top with bean sprouts, cilantro, Thai basil, sea salt, black pepper, and a squeeze of lime.