Prepare Broth
Slice one onion quarter thinly; set aside.
Bring remaining 3 onion quarters, beef broth, chicken broth, water, fish sauce, ginger, cinnamon stick, sugar, star anise, and cloves to a boil.
Simmer uncovered 30 minutes.
Strain broth through a fine mesh strainer. Discard solids.
Cook Noodles
Boil water. Off heat, add noodles. Let sit, stirring, 5 to 10 minutes until soft and pliable.
Drain and rinse with cold water.
Cook Beef and Assemble
Bring strained broth to a boil. Add noodles; cook 30 seconds to 1 minute until tender.
Divide noodles evenly into bowls.
Simmer broth and add sliced beef; cook 1 minute until no longer pink.
Divide beef between bowls.
Season broth with salt, if necessary.
Ladle broth over noodles and beef. Top with reserved sliced onions, bean sprouts, and cilantro.
Serve with lime wedges, hoisin, and sriracha.
