The broth for the gravy may be made up to 3 days in advance. Lightly coat the bottom of a 12" skillet with extra-virgin olive oil and heat over medium-high. Add the neck and giblets from the turkey and mixed chicken legs and thighs; season to taste with salt and pepper. Brown on both sides; transfer to a 6-quart pot. Pour half of the fat out of the skillet; heat over medium-high. Stir in 2 chopped yellow onions, 2 cloves crushed garlic, 2 whole cloves, 1 chopped carrot, and 1 chopped celery rib with leaves and cook until just browned, 12–14 minutes. Remove skillet from heat and add 1⁄4 cup of the calvados and 2 cups of the wine. Return to heat, bring to a boil, and scrape up the brown bits on the bottom of the skillet. Transfer the vegetable mixture to the 6-quart pot of meat. Add enough water to cover the mixture to a depth of 1"; bring to a slow simmer. Partially cover and cook, without stirring, for 4–5 hours. (Add more water as necessary to keep solids covered.) Remove from heat, let cool, strain (as shown), and refrigerate broth. You should have about 12 cups.
A day before serving, brine the turkey, calculating 1 hour of brining for each pound. In a large plastic brining bag or stockpot, combine 1 cup of the salt, brown sugar, and chile powder. Put 2 cups of the cider, 35 cloves garlic, and 4 unpeeled, cored, and coarsely chopped granny smith apples into a food processor and purée. Add purée to the brining bag along with 6 cups of the cider and 4 quarts cold water. Whisk to dissolve the salt and sugar.
Put turkey into brining bag. The turkey must be kept cold (brine should be 33°), so refrigerate it or bury the bag in ice in an oversize cooler, adding ice as necessary. Before cooking, bring the turkey close to room temperature for the shortest roasting time. (Calculate 10 minutes' roasting time per pound.)
Remove the oven's center rack and arrange the remaining rack as low as possible. Heat oven to 450°. Choose a large shallow roasting pan, ideally 2" deep; if the pan is too deep, the turkey will steam instead of roasting. In the pan, cluster together remaining celery ribs halved crosswise, leaves removed; remaining 3 carrots halved crosswise, and remainign 3 onions cut into thick rounds so that the vegetables become a sturdy rack for the turkey. Scatter 1 unpeeled, cored, and coarsely chopped granny smith apple and 1 1⁄2 cups basil leaves over the top. Add 4 cups of the wine to cover the bottom of the pan with 1⁄2" of liquid
Remove the turkey from the brine and pat it dry with paper towels. Set the turkey on the vegetables breast down (a technique that draws juices down into the breast while also protecting the meat from the heat) and tuck remaining unpeeled, cored, and coarsely chopped granny smith apple and remaining 1⁄2 cup basil leaves into the cavity. Dot the turkey with butter and dust all over with 1⁄2 tsp. pepper. Begin roasting.
As the bird cooks, baste it with the pan juices every 20 minutes using a spoon. After the first hour, remove the roasting pan from oven and, using two pot holders, carefully turn the turkey breast side up. Baste it with the pan juices and continue roasting. (Cover the turkey loosely with foil if it threatens to burn.) When an instant-read thermometer inserted in a thigh (without touching bone) reaches 165°–170° (after about 2 hours), move the turkey to a platter and let it rest in a warm place for 20 minutes.
Meanwhile, set the roasting pan over 2 burners to make the gravy. Skim off excess fat from pan juices and remove two-thirds of the vegetables from the pan. Cut the rest of the vegetables into small pieces. Add remaining 1⁄3 cup calvados, remaining 1⁄2 cup wine, and remaining 1⁄3 cup cider. Bring to a boil over high heat and, using a wooden spatula to scrape up all the caramelized bits, cook the liquid down to a syrup, 6–8 minutes.
Remove broth from refrigerator; skim off fat. Reheat all but 1 cup. Add two-thirds of the heated broth to the pan. Boil, stirring constantly, until reduced by half, about 15 minutes. Stir the remainder of the heated broth into the pan and bring to a boil. To thicken the gravy, add flour to a tall glass. Stir the 1 cup of reserved, chilled broth into the flour until there are no lumps. You've made a slurry. Whisk it into the bubbling gravy. Keep simmering and whisking until gravy is smooth and thick enough to lightly coat the back of a spoon, about 20 minutes. Now taste it. If you taste raw flour, simmer the gravy for another minute.
Stir 8 torn basil leaves into the gravy and season with kosher salt and freshly ground black pepper, if necessary. Pour the gravy into a bowl or another serving vessel. Carve the turkey and arrange on a large platter. Serve with the gravy passed separately.