Place chicken and 5 quarts of water into a large stock pot and bring to a boil over high heat. Skim the foam that rises to the top. Reduce the heat to medium-low and simmer, add the ginger, 3/4 of the onions and garlic. Cook until chicken is cooked through, about 35 to 40 minutes. Transfer the chicken to a plate and allow to cool. When cool enough to handle, remove the meat from the bones. Return the bones to the pot and continue to simmer until the broth has reduced by half, about 1 1/2 hours. Reserve the chicken meat on the side.

Soak the wood ear mushrooms in a bowl of warm water until soft, about 30 minutes. Drain, slice and set aside. Heat peanut oil in a 12-inch skillet, over medium heat. Thinly slice the remaining onions, add to the pan and cook until translucent, 4 to 5 minutes. Add the shitake mushrooms and cook until mushrooms are soft, about 2 minutes. Add the shrimp and cook until just pink, about 1 minute. Remove from the pan and set aside.

In a medium size saucepan, bring 4 cups of water to a boil. Add the rice, reduce the heat to medium and cook, stirring occasionally, until rice is al dente (tender but still a little firm) about 8 minutes. Drain the rice in a colander and rinse under cold water until cool. Set aside.

Strain the chicken broth into a medium pot, discarding the bones and vegetables. Add the drained rice, shredded chicken, and wood ear mushrooms; bring to a boil over high heat. Reduce the heat to medium-low and simmer until rice is very soft, about 10 to 12 minutes. Rinse tapioca in cold water, and then add to soup. Continue to simmer the soup, stirring frequently, until the tapioca turns transparent and soup begins to thicken, about 30 minutes longer.

Add the shrimp, onion and shiitake mushroom mixture to the soup, season to taste with salt and freshly ground white pepper, and simmer for another 2 or 3 minutes. Ladle into warm bowls and garnish with scallions, cilantro and basil and a dash of fish sauce, all to taste.