Slice 1 onion quarter as thin as possible; set aside until ready to serve. Bring broth, water, fish sauce, sugar, ginger, cinnamon, star anise, cloves, and remaining 3 onion quarters to boil in medium saucepan, then reduce heat to medium-low and simmer for 30 minutes.
While broth simmers, pour 2 quarts boiling water over noodles in bowl and stir to separate. Let noodles soak until soft and pliable but not fully tender, stirring once halfway through soaking, 8 to 10 minutes. Drain noodles and rinse with cold water until water runs clear, shaking to remove excess water.
Strain broth through fine-mesh strainer into 4-cup liquid measuring cup, adding water as needed to equal 3 cups. Discard solids. Combine noodles and broth in now-empty saucepan, return to boil, and cook until noodles are tender, about 1 minute. Season with salt and pepper to taste.
Stir in thinly sliced onion and steak. Serve immediately, topped with sprouts, cilantro, and extra fish sauce, and accompanying lime wedges.