Sheet Pan Roasted Chicken with Root Vegetables

Brussels sprouts (, trimmed and halved)

red potatoes (, unpeeled, cut into 1-inch pieces)

shallots (, peeled and halved lengthwise (I only used 6))

medium carrots (, peeled and cut into 2-inch lengths, thick ends halved lengthwise)

garlic cloves (, peeled)

vegetable oil

minced fresh thyme or 1 1/2 tsp dried (, divided)

minced fresh rosemary or 3/4 tsp dried (, divided)

sugar ((I omitted this))

Salt and pepper

unsalted butter (, melted)

lbs bone-inch chicken pieces ((2 split breasts cut in half crosswise, 2 drumsticks, and 2 thighs), trimmed*)