Preheat the oven to 375°F. Line the bottom of a large pan with with aluminum foil then fit with rack. (You can also use a grill pan or broiler pan sprayed with cooking spray.)
In a small bowl mix together barbecue seasoning and brown sugar. Drizzle the chicken pieces with olive oil then rub liberally with the seasoning on all sides.
Place skin side down on the rack or pan. Bake for 30 minutes.
While the chicken is baking on the stovetop in a medium saucepan saute the minced onion in 1 Tbsp of butter over medium high heat. Saute until softened, around 2-3 minutes.
To the saucepan add ketchup, maple syrup, light brown sugar, soy sauce, apple cider vinegar, liquid smoke, garlic powder, onion powder, red pepper flakes, barbecue seasoning([use the same as rub), cumin and salt. Simmer on low uncovered for 15 minutes to reduce and thicken. (Skip this if using a prepared barbecue sauce.)
After the chicken has baked for 30 minutes, remove from the oven and drain the juices from the pan.
Baste the chicken on all sides with sauce. Turn skin side up and drizzle the top with sauce.
Return to oven and bake for another 10-15 minutes or until the juices run clear. (If the breast pieces are large remove the wings, back and legs to a platter at 40 minutes and keep warm.)
Continue to cook the breast pieces checking in 5 minute increments, until the juices run clear or the chicken has reached an internal temperature of 165°F.
Char: At the end of cooking, increase the oven temperature to broil, and move the oven rack up. Broil the chicken for 3-4 minutes until the skin is charred. Keep a close eye on the chicken. Remove from the oven, brush with sauce and rest loosely tented with foil for 10 minutes before serving.
Serve leftover sauce on the side, if desired.