Make the chicken: Combine the brown sugar, chili powder, paprika and cumin in a small bowl. Season the chicken all over with 1 tablespoon salt and 1 teaspoon pepper, then rub all over with the spice mixture. Cover and refrigerate 1 to 2 hours.
Meanwhile, make the barbecue sauce: Whisk the ketchup, vinegar, brown sugar, orange juice, garlic, molasses, hoisin sauce, mustard and chili powder in a small saucepan until smooth. Bring to a boil, then reduce the heat to a simmer and cook until slightly thickened, 10 to 15 minutes. (You should have 1 1/4 to 1 1/2 cups sauce.)
Remove the chicken from the refrigerator 30 minutes before grilling. Preheat a grill to medium and oil the grates. Grill the chicken, covered and turning occasionally, until lightly charred and a thermometer inserted into a drumstick (without touching the bone) registers 170 degrees F, 35 to 45 minutes, brushing with some of the barbecue sauce during the last 10 minutes of cooking. Transfer to a platter and brush with more barbecue sauce. Serve with the remaining sauce.