In a dry 3-qt. or larger saucepan over medium heat, combine the star anise, cloves, cinnamon stick, and fennel seeds. Toast the spices, shaking the pan occasionally, until quite fragrant, 1 to 2 min. Add the chicken and beef broths, fish sauce, and ginger, and bring to a boil over high heat. Reduce the heat to medium low or low, cover, and simmer gently for 30 min.
Meanwhile, soak the rice noodles in cold water for 20 minutes. Bring 2 qt. water to a boil in another 3-qt. or larger saucepan. Drain the rice noodles and add them to the boiling water. Give the noodles a quick stir and cook until just tender, 1 to 2 min.--don't overcook or the noodles will get gummy. Drain the noodles and portion them into four large soup bowls.
Portion the steak, scallions, cilantro, basil, and shallot into the four bowls, scattering them over the noodles. Strain the broth into a heat-proof container, preferably one with a pouring spout, such as an 8-cup Pyrex measuring cup. You should have about 5 cups broth; if not, add water to equal 5 cups and quickly reheat the broth if necessary. Divide the broth among the four bowls, pouring it over the noodles and other ingredients. Top with the bean sprouts. Serve with the lime wedges and chile paste or chiles (if using) on the side for diners to add individually to taste.