How to Make It
In a large saucepan, cover the chicken with 8 cups of water (it should come two-thirds of the way up the side of the pan) and bring to a boil over high heat. Add the salt, then reduce the heat to moderately low and simmer gently for 20 minutes, skimming the foam occasionally.
Meanwhile, in a small saucepan, bring the soy sauce, lemon juice and vinegar to a simmer over high heat. Remove the ponzu sauce from the heat.
Transfer the chicken to a plate. Add any root vegetables to the simmering broth and cook until tender, about 5 minutes. Using a slotted spoon, transfer the vegetables to 4 bowls. Pull the chicken meat into large pieces, discard the skin and bones and add the chicken to the bowls.
Add any leafy greens to the simmering broth and cook until just wilted and bright green, about 1 minute. Transfer the greens to the bowls and add 1/2 cup of broth to each. (Keep the remaining broth simmering in the saucepan.) Season each serving with some of the daikon, ginger, togarashi and ponzu sauce and serve.
When everyone has finished eating the chicken and vegetables, stir the noodles into the simmering broth until hot, then divide the noodles and broth among the bowls, season with more daikon, ginger, togarashi and ponzu sauce and serve.
Togarashi, a Japanese blend of chiles and sesame seeds, is available at Asian markets.