Rinse chicken. Mix together water, sugar and salt in a large container and place the chicken in the mixture. Cover and refrigerate for 3-4 hours.
Toast the fennel seeds, coriander seeds and peppercorns in a small, heavy pan over medium heat. This is very quick. Add the red pepper flakes, and toss. Using a small spice mill or a coffee grinder dedicated to grinding spices, grind only the fennel, coriander, pepper and chili flakes. Pour into a bowl and toss with the chili powder, cinnamon and salt.
Remove chicken from brine, rinse and pat dry. Rub chicken with olive oil and generously with spice rub. Pre-heat the oven to 450 degrees F. Place the chicken, breast-side down, on a rack in a roasting pan and roast for 15 minutes. Turn the chicken breast-side up.
Reduce the oven temperature to 375 degrees F and continue roasting until the juices run clear when a thigh is pierced with a skewer (50-55 minutes longer). Transfer the chicken to a platter and let it rest for at least 15 minutes before carving. Remove rack from the roasting pan and place on stove over medium heat. Swirl in butter. Deglaze pan with sherry vinegar. Add chicken broth and reduce liquid by half. Remove from heat and spoon over sliced chicken.