Remove the neck and giblets from the turkey and reserve for making stock.
Place the turkey on a baking sheet. Tie the legs together (if not already held together) and tuck the wings underneath the turkey, using small skewers to secure.
In a small bowl, stir together the paprika, smoked paprika, rosemary, thyme, ground pepper, garlic powder and salt. Add the maple syrup and olive, and stir to combine.
Starting at the neck end of the turkey, slide your hands under the breast skin to loosen. Smear half of the rub underneath the breast skin. Smear the other half of the rub over the entire topside of the turkey.
Cover the turkey with plastic wrap and refrigerate over night.
Remove the turkey from the refrigerator 1 hour before cooking to bring to room temperature.
Preheat the oven to 350 degrees F.
Place the turkey on a rack in the roasting pan, breast side up. Scatter the shallots around the turkey, on the bottom of the roasting pan. Place the carrot, celery and onion quarters in the cavity of the turkey.
Cover the breasts with foil and place the turkey in the oven.
Roast the turkey for 2 hours, basting it with ½ cup chicken broth every 30 minutes.
Remove the foil from the breast. If the legs are browning too much, cover each drumstick with foil.
Roast the turkey until a thermometer inserted in the deepest part of the thigh (be sure not to hit the bone) registers 170 degrees F, basting every 30 minutes with the pan drippings, about 1 hour more. If any sections of the breasts are browning too much, cover those sections with foil.
Remove the turkey from the oven, transfer it to a platter and let rest for 20 minutes before carving.
Remove the carrot, onion and celery from the cavity and discard.
Remove the shallots from the pan and serve with the gravy. Use the remaining brown bits on the bottom of the pan for making the gravy (I typically make the gravy right in the roasting pan, set over two burners.)
Carve and serve.