Preheat oven to 400 degrees. With your fingers, loosen the skin on the chicken breast. Cut the goat cheese into 4 1/2-inch-thick rounds. Carefully place rounds in a decorative pattern under skin, and press a sage leaf into each round.
Stuff chicken with herbs, and truss with kitchen twine. Season with salt and pepper. Place on a rack in a roasting pan. Surround chicken with onions, shallots, and garlic.
Roast, uncovered, and basting occasionally with melted butter, until chicken is cooked through, 1 hour to 1 hour and 20 minutes.
Place carrots and parsnips on a baking sheet. Drizzle with olive oil, and season with salt and pepper. Transfer to oven, and roast until tender, about 1 hour. Serve chicken with vegetables; garnish with herbs.