Put the chicken in a large donabe, Dutch oven or saucepan and cover with 8 cups cold water. Bring to a boil over high heat. Add the salt, then reduce the heat to medium-low. Simmer gently for 20 minutes, skimming any foam that rises to the surface.
Meanwhile, make the ponzu sauce: Combine the soy sauce and vinegar in a small saucepan and bring to a boil over high heat. Remove from heat and stir in the lemon juice, then cool to room temperature and reserve.
Prepare the vegetables: Seed the squash and cut into 2-inch-wide wedges. Cut each wedge into ⅓-inch-thick slices. Trim the bok choy and cut larger leaves in half. Peel the daikon and ginger and grate on a Microplane zester or Japanese ginger grater into separate bowls.
Transfer the chicken to a plate; keep the broth simmering. Add the squash to the broth and simmer until tender, 8 to 10 minutes. While the squash cooks, prepare the udon according to the package’s directions. Discard the chicken skin and bones. Pull the meat into large pieces and divide among 4 serving bowls along with the udon.
Stir the bok choy into the simmering soup and cook until just wilted and bright green, about 1 minute. Divide the vegetables and broth among the bowls with the chicken and sprinkle with togarashi. Serve with the daikon, ginger and ponzu sauce, seasoning each bowl or spoonful to taste.
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