Step 1 If using dried chickpeas, put them in a small saucepan and add 3 cups water. Cover and bring to a boil over medium heat. Simmer over low heat for 1 hour, adding additional hot water if necessary to keep them covered. Add a pinch of salt and simmer until tender, about one to 1 1/2 hours more. Remove from heat and set the chickpeas aside, still in their liquid. If using canned chickpeas, drain and rinse the chickpeas, cover and set aside.
Step 2 Cut off the dark green tops of the leek and rinse them thoroughly. Put the leek greens in a couscous or soup pot or a large stew pan. Set aside the rest of the leek to use later.
Step 3Add the chicken to the leek greens in the pot. Add the quartered onion, celery ribs and enough water to cover the ingredients, about 8 to 10 cups. Bring to a boil over high heat, skimming any foam that forms on the surface. Reduce the heat to low and simmer for an additional 10 minutes, skimming any foam. Add the sprigs of cilantro and parsley, the saffron and a pinch each of salt and pepper.
Step 4Cover and simmer over low heat until the chicken is just tender and the meat near the bone is no longer pink, about 45 minutes; when the chicken is pierced in its thickest part with the point of a knife, any juices that come out should be clear, not pink. Discard the soup vegetables and herb sprigs. Remove the chicken with a slotted spoon and cool the chicken and broth separately. (The recipe can be prepared up to this point a day or two in advance; cover and refrigerate the broth, chicken and chickpeas until needed.)
Step 5Skim any fat from the surface of the broth, then bring the broth back to a boil over high heat. Add the tomatoes, kabocha squash, carrots and turnips to the broth. Cover and simmer over medium-low heat for 15 minutes.
Step 6While the broth is simmering, cut the white and light green part of the leek in half lengthwise and rinse it thoroughly, checking to make sure there is no sand between the layers. Cut the leek crosswise into 1 1/2- to 2-inch pieces and check again for sand.
Step 7Add the leek to the broth. Add the cooked chickpeas, along with their liquid if desired, or the drained canned chickpeas. Return broth to a simmer. Cover and cook over low heat for 5 minutes, then add the Mexican squash and return to a simmer. Cover and cook until the vegetables are tender but not falling apart, about 7 minutes.
Step 8Remove 4 cups of the vegetables with a slotted spoon. Remove the kabocha squash pieces and cut them into bite-sized cubes. Add them to the other vegetables.
Step 9To reheat the chicken, add the pieces to the hot broth and simmer them gently until heated through, 10 to 15 minutes.
Step 1 0Heat the oven to 400 degrees. Place the removed 4 cups cooked vegetables in a shallow 2-quart baking dish, drizzle with 1 tablespoon olive oil and sprinkle with the sugar. Bake the vegetables until they brown lightly, about 20 minutes. Sp