In a saucepan over high heat, bring the cider to a boil. Cook until it is reduced to 1 cup, about 30 minutes. Set aside ½ cup of the reduced cider for the gravy. Mix the butter and thyme into the remaining reduced cider and refrigerate until cold.

Position a rack in the lower third of the oven and preheat the oven to 325°F.

Pat the turkey dry and place on a rack in a roasting pan. Spread the cider butter inside and over the outside of the turkey. Sprinkle with salt and pepper. Tie the legs together. Tuck the wing tips under the body. Roast for 45 minutes. Baste the turkey with the pan juices. Continue roasting, basting every hour, until an instant-read thermometer inserted into the thickest part of a thigh away from the bone registers165°F, about 2¼ hours longer. Transfer the turkey to a platter, tent with aluminum foil, and let rest for 30 minutes. Pour the pan juices into a large measuring cup; skim off and discard the fat.

For the gravy: In a saucepan over medium-high heat, melt the butter. Add the shallots and thyme and sauté until the shallots are golden brown, about 8 minutes. Add the flour and cook, stirring frequently, until browned, about 4 minutes. Add enough stock to the pan juices to measure 5 cups. Gradually whisk the stock mixture into the flour mixture, then bring to a boil, whisking frequently. Mix in the reserved ½ cup reduced cider and boil until thickened, about 10 minutes. Mix in the applejack and return to a boil. Season with salt and pepper. Pour the gravy into a warmed sauceboat.

Carve the turkey and serve with the gravy.