Tip:Indirect grilling is a must for chicken on the bone so the chicken can cook through before the outside burns. Don’t glaze the chicken until just before it’s done, or the glaze will burn; watch for flare-ups after the glaze goes on.
In a small bowl, combine the brown sugar, paprika, garlic, 2 tsp. of the five-spice, fennel, mustard, 1 Tbs. salt, and 2 tsp. pepper. Put the chicken pieces in a 9x13-inch baking dish and rub the spice mix all over the chicken. Cover and refrigerate for at least 2 hours and no more than 6 hours.
Prepare a charcoal or gas grill fire for indirect cooking over medium heat (325°F to 375°F). In a small bowl, combine the hoisin, maple syrup, soy sauce, honey, sesame oil, ginger, and the remaining 1/2 tsp. five-spice powder.
Lightly brush the chicken pieces with the peanut oil and arrange skin side down over direct heat. Cover and cook until grill marks form, 3 to 5 minutes. If the chicken flares up, immediately move it to indirect heat. Flip the chicken and mark the other side, 2 minutes more. Move the chicken to the cooler side of the grill to finish cooking over indirect heat. Cover and cook, occasionally rearranging the pieces to ensure even cooking, until an instant-read thermometer registers 165°F (breast pieces) to 170°F (leg pieces), 30 to 45 minutes.
Generously brush the glaze on the chicken and flip glaze side down over to the hotter part of the grill. Cook until the glaze is bubbly and deep red, 30 to 60 seconds. Brush more glaze on the top of the chicken, flip, and cook for 30 to 60 seconds more. Serve immediately.