ADJUST oven rack to upper-middle position; PREHEAT oven to 475 degrees.

TOSS Brussels sprouts, potatoes, shallots, carrots, garlic, oil, 2 tsp fresh thyme, 1 tsp fresh rosemary, sugar, 3/4 tsp salt, 1/4 tsp pepper together in a large mixing bowl.

In a small mixing bowl, STIR together melted butter, remaining 2 tsp fresh thyme, remaining 1 tsp fresh rosemary, 1/4 tsp salt and 1/8 tsp pepper.

PAT chicken dry with paper towels; SEASON with salt and pepper.

PLACE vegetables in a single layer on an 18 by 13-inch rimmed baking sheet, arranging Brussels sprouts in center.

PLACE chicken, skin side up, on top of vegetables, arranging breasts pieces in center and thighs and drumsticks around perimeter of sheet.

BRUSH chicken with herb butter. ROAST until breasts register 165 degrees and drumsticks/thighs register 175 degrees, 35 - 40 minutes, rotating pan halfway through roasting.

REMOVE sheet from oven, TENT loosely with aluminum foil, REST 5 minutes. TRANSFER chicken to platter or plates.

TOSS vegetables with pan juices, SEASON with salt and pepper to taste, TRANSFER to platter or plates and serve warm.