Preheat the oven to 325° F.
Fill the cavity of the turkey with stuffing.
Rub the outside of the turkey with 3 tablespoons of the butter, the tarragon, salt, and pepper.
Pour 6 cups of broth into the bottom of the roasting pan.
Bake the turkey for about 4 hours, basting every 30 minutes or so.
If the bird starts getting too brown, cover with a foil tent.
(Check for doneness with a meat thermometer—it should register somewhere between 162°F and 170°F.) When the turkey is cooked, remove it from the pan and keep warm.
Pour off most of the fat in the roasting pan, until only 2 to 3 tablespoons remain.
Heat the remaining 2 cups of broth.
Place the roasting pan on the stovetop over high heat and add the hot broth, scraping the brown bits off the bottom of the pan.
Reduce by half and remove from the heat.
Add the remaining butter, one tablespoon at a time, until well combined.
Carve the turkey and serve with the stuffing and delicious tarragon-flavored gravy.
Be sure to put lots of sauce on the plate so the other side dishes are flavored by these great-tasting juices.