Dry-brine the turkey: Pat the turkey dry and put on a rimmed baking sheet. Rub 2 tablespoons salt, 1 teaspoon pepper, the garlic powder and dried dill all over the turkey. Refrigerate, uncovered, overnight.
Position a rack in the lowest part of the oven, remove the other racks and preheat to 350 degrees F. Toss the thyme, shallots, carrots, celery and turkey neck with the olive oil in a large roasting pan; set a rack on top. Stuff the turkey cavity with the apple, garlic and fresh dill and tie the legs together with kitchen twine. Place the turkey breast-side up on the rack and tuck the wings under the body. Let sit at room temperature 30 minutes.
Roast the turkey 1 hour, then baste with the pan drippings. Roast for 1 more hour, basting every 30 minutes. Melt the butter with the sweet paprika and hot paprika in a small saucepan over medium heat. Brush the turkey all over with about half of the butter. Continue roasting until the skin is crisp and a thermometer inserted into the thigh registers 160 degrees F to 165 degrees F, 15 to 60 more minutes, brushing with more of the butter during the last 10 minutes. (Add the broth to the roasting pan if the drippings are getting too dark.) Remove the turkey from the oven and brush with the remaining butter. Transfer the turkey (on the rack) to a rimmed baking sheet and let rest 30 minutes before carving. Use the pan drippings for gravy.