Place the turkey, breast side up, in a large plastic bag or oven-roasting bag. Add the hot sauce, 1 tsp. salt and 1 tsp. pepper to the buttermilk container; shake to combine. Pour the buttermilk mixture over the turkey, avoiding the cavity. Seal the bag, transfer to the refrigerator and let marinate, turning the turkey over once, for 8 hours or overnight.
Remove the turkey and pat dry inside and out. Rub the skin with 1 tbsp. oil; season with salt and pepper. Let rest at room temperature.
Preheat the oven to 400°. Using kitchen twine, tie the turkey legs together at their ends. Tuck the wings behind the back of the turkey, if desired. Place the turkey, breast side up, on a rack set in a large roasting pan. Roast, basting once with the pan juices, for 1 hour. Lower the heat to 350° and roast, basting every half hour, until an instant-read thermometer registers 155° when inserted into the thigh, 1 to 1 1/2 hours more. If the turkey is over-browning, tent loosely with foil. Remove from the oven, tent with foil and let rest for 30 minutes.
In a large pan, heat the remaining 1/3 cup oil over medium heat. Add the onions, garlic, 1/2 tsp. salt and 1/4 tsp. pepper and cook, stirring frequently, until soft and browned, about 35 minutes. Add the flour; cook, stirring constantly, for 2 minutes. Add 1/2 cup chicken broth and cook, stirring, until thickened. Add the remaining 1 1/2 cups broth and bring to a boil. Lower the heat and simmer for 5 minutes. Serve the gravy with the turkey.