Preheat the oven to 375°F.
2. Make the glaze: Whisk together the Jack Daniel’s, soy sauce, vinegar, mustard, and brown sugar in a medium bowl; set aside.
3. Place the turkey, breast side up, on a rack in a large roasting pan. Season all over with salt and pepper. Tuck the wings underneath the body and tie the legs together. Spread a thick layer of margarine all over the turkey. Pour the chicken broth into the bottom of the roasting pan.
4. Roast the turkey for 30 minutes. Pour and brush about half the glaze all over the turkey and return it to the oven. Roast for 30 minutes more. Pour and brush the remaining glaze over the turkey and return it to the oven. Roast for another 60 minutes. Check the temperature with a thermometer inserted into the thickest part of the thigh. Continue roasting until the temperature registers 165°F on an instant-read thermometer. Remove the turkey from the roasting pan, and let it rest on a cutting board, loosely tented with foil, for 15 to 20 minutes before carving.
5. While the turkey is resting, prepare the gravy: Pour the accumulated pan juices into a bowl or a fat separator. Let sit for a minute or two to allow the fat to separate and rise to the top. If you are using a bowl, carefully tilt it and skim off the fat from the pan juices with a large spoon, reserving 2 tablespoons and discarding the rest, or use a fat separator. Set aside the pan juices. Return the 2 tablespoons fat to the roasting pan. Whisk in the flour slowly to prevent lumps from forming. Cook on top of the stove over medium heat, stirring up any browned bits, until the flour is incorporated and the mixture is smooth. Gradually add 2 to 3 cups of the pan juices to the pan, stirring continually. Cook until the gravy is thickened, about 5 minutes. If you’d like it a little thinner, add up to 1 additional cup of the pan juices. Season with additional pepper, if desired. Strain the gravy through a fine-mesh sieve.