Pour the chicken (or turkey) broth into a saucepan. Bring to a boil, reduce heat to low and let simmer and reduce while the turkey roasts. (You want to reduce it by approximately 1/3 or to 4 cups). Turn the heat off when that is accomplished.)
Lightly oil a 13 x 9-inch baking dish or roasting pan. Preheat oven to 350 degrees.
Carefully butterfly the turkey breast, open it and lay it flat on a cutting board or another flat surface. With the tip of a boning knife, carefully and very lightly cut some shallow slits in the opened breast just to get it to lie flatter and create more surface area. Place a gallon-size zipper-top over the opened turkey breast and gently pound it with a meat mallet or rolling pin to flatten it out some more.
Season the flattened turkey breast with black pepper. Spread the reserved 2 cups of stuffing over the flattened breast, leaving a 1-inch border.
Turn the right side of the turkey breast over the filling then bring the left side over. Secure with butcher's twine, making sure the filling is securely inside and the skin is nicely flattened and secured over the top of the breast.
Place in the prepared roasting pan. Spread 4 tablespoons of the butter over the turkey breast. Roast for 1 hour. Baste with the buttery pan juices once during this time.
Place the baking dish of the remaining stuffing in the oven alongside the turkey. Baste with the buttery pan juices while the oven door is open. Continue roasting the turkey for another 20-30 minutes or until an instant-read thermometer registers 160 degrees IN THE CENTER OF THE STUFFING.
Remove from the oven, transfer to a platter and tent with aluminum foil and let rest for 10-15 minutes. (Carryover cooking while resting will take the breast to 165 degrees.) Check the stuffing so it doesn't get overly browned and cover with aluminum foil or another cover if needed.
Carefully pour any brown buttery drippings into a saucepan. (Avoid any that are overly browned.)
Add the remaining 2 tablespoons of butter to the saucepan and melt over medium heat.
Add the flour and cook 1-2 minutes, whisking constantly.
Pour in the reduced broth. Bring to a boil, reduce heat to medium and cook until thickened. Season with salt and black pepper if needed.
Slice the turkey breast and serve the stuffing and gravy with the turkey breast.