Step 1 Place the onion, ginger, saffron, 1/2 teaspoon of salt, the oil and 2 cups of water in a food processor and process to a smooth liquid.
Step 2 Place the liquid in a saucepan just large enough to hold the chicken, lay the chicken in it, cover and cook over medium heat until very tender and the meat is falling off the bone, 1 hour, 15 minutes to 1 hour, 30 minutes. From time to time, remove the lid and baste the chicken with the sauce. Add more water if the sauce is in danger of drying up.
Step 3Meanwhile, peel and seed the pumpkin or squash and cut it into 1-inch pieces. Place the pieces in a large skillet with 1/2 cup of water and the butter. Sprinkle with the remaining 1/2 teaspoon of salt. Simmer over low heat until very tender, 40 to 50 minutes. Remove the squash from the skillet, place it in the food processor with the honey and cinnamon and process to a puree.
Step 4Serve the chicken in the sauce or with it on the side. Serve the pumpkin puree on the side or mix it into the sauce.