Rinse duck in cold water and pat dry; rub all over with remaining spice mixture and olive oil. Season generously inside and out with salt and pepper. Place duck, breast side up, on top of vegetables in roasting pan. Add neck and organs (if using), along with thyme, bay leaves, and 2 cinnamon sticks. Tuck wings behind neck, cover pan tightly with aluminum foil, and roast for 2 hours.
In a saucepan, combine cherries, red wine, sugar, and remaining whole star anise and cinnamon stick. Cook over low heat until cherries are soft and wine has reduced to a syrup, about 30 minutes. Reserve about 3 tablespoons for glazing duck. Transfer rest to a small serving bowl for use as a compote; set aside and keep warm.
After duck has cooked for 2 hours, remove foil and baste with pan juices. Add garlic, replace foil, and cook until meat starts pulling away from the bone, about 2¼ hours more.
Remove from oven and discard foil. Brush duck with cherry-wine syrup. Increase temperature to 375°, and roast until skin gets crispy and dark brown, at least another 15 minutes.
Carefully transfer whole duck to a large serving platter; let it rest uncovered while assembling other elements of dish. Use a slotted spoon to transfer vegetables to a large bowl, letting excess fat drip away. Pick off neck meat and thinly slice giblets; add them to vegetables. Mash together, and season to taste with salt and pepper. Transfer to a serving bowl.
Carve duck at the table. Serve with mashed vegetables and compote.
Adapted from The Paley's Place Cookbook, by Vitaly Paley and Kimberly Paley with Robert Reynolds, copyright © 2008 (with permission from Ten Speed Press).