Dry the cavity and outside skin of the turkey with paper towels.
Season the inside cavity with 1 tablespoon of the salt and pepper mix you've prepared in a small bowl, reserved specifically for the turkey.
Pour 1 cup of balsamic vinegar liberally over the entire turkey, and allow the turkey to marinate with the vinegar at least 20 minutes, at room temperature.
Preheat oven to 450-degrees.
Stuff the cavity of the bird with the chopped onion, carrot, and celery.
In a medium bowl, stir together the softened butter, the minced fresh herbs, and the remaining salt and pepper from the small bowl reserved for the turkey.
Gently run your hand between the turkey skin and the meat of the breast and lift the skin gently.
Pour ¼ cup of the remaining balsamic vinegar over the breast meat of the turkey and also rub approximately 3 tablespoons of the herbed butter mixture over the meat, under the skin.
Replace the skin on the breast and liberally slather the remaining herb butter mixture over the breast and leg area of the turkey.
Roast the turkey, uncovered, for 45 minutes.
Remove the turkey from the oven, and reduce the oven temperature to 350-degrees.
Add the chicken broth to the roasting pan, spooning the pan juices liberally over the turkey, and return the turkey back to the oven until the internal temperature of the turkey (using a meat thermometer inserted into the thigh area of the turkey) reads 165-degrees (approximately 2½ - 3 hours). *Note - If during that time the turkey appears to be browning beyond your liking, cover it with aluminum foil and continue roasting until the internal temperature reaches 165-degrees.
Remove the turkey from the oven and allow it to rest for at least 30-45 minutes before slicing.
Use the juices in the pan to make gravy, if desired.
*See notes if you plan on making the turkey in advance.