Mix together the salt, lemon zest, pepper flakes and thyme in a small bowl. Rub the turkey all over with the mixture, inside, outside and under the skin. Stuff the cavity with the shallots, lemon halves and thyme and rosemary sprigs. Tie the turkey's legs together with butcher's twine. Loosely cover the bird with parchment paper and allow it to dry-brine in the refrigerator for at least 24 hours and up to 48 hours.
Preheat the oven to 350 degrees F. Remove the turkey from the refrigerator 30 minutes before cooking to allow it to come to room temperature.
Lay the celery across the bottom of a rimmed baking sheet and place the bird on top. Shingle the prosciutto slices over the entire bird, tucking them into the leg creases and making sure the bird is entirely covered. Using toothpicks, secure the prosciutto in 6 spots. Add the chicken broth to the bottom of the pan. Place a piece of parchment over the bird, then cover the pan with aluminum foil. Roast for 3 hours.
Remove the foil and baste the bird with some of the pan drippings. Raise the oven temperature to 400 degrees F and roast for an additional 45 minutes to an hour, until the prosciutto is crisp and the turkey registers 155 degrees F at the thigh on an instant-read thermometer. Remove from the oven and let rest for 20 minutes before carving.
Meanwhile, strain the pan juices into a small saucepan and let sit for 5 minutes before skimming the fat. Add the maple syrup and balsamic vinegar; stir to combine. Bring to a simmer over medium heat and cook for 5 minutes to reduce slightly. Serve alongside the turkey.