Preheat the oven to 375 degrees F, with a rack in the position third from the top and another just below it.
Combine 4 tablespoons of the butter, 1 tablespoon of the parsley, the thyme and garlic in a small bowl. Season with salt and pepper.
Place the turkey, skin-side up, on a rack set in a rimmed baking sheet. Rub the herb butter over the turkey and underneath the skin. Sprinkle liberally with salt and pepper.
Toss together the cippolini, vinegar and oil in a 1-quart ovenproof baking dish. Season with salt and pepper.
Place the turkey on the higher oven rack and the cippolini on the rack below. Roast until the cippolini are cooked through and tender and an instant-read thermometer inserted into the thickest part of the turkey registers 155 degrees F, 45 minutes to 1 hour. Stir the remaining 2 tablespoons butter into the cippolini. Let the turkey rest for 10 minutes before slicing.
To serve, cut the turkey off the bone and slice thinly. Divide among plates and top with the cippolini. Garnish with the remaining 1 tablespoon parsley.
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