Brine turkey for 12 to 18 hours before roasting; follow your preferred turkey brine recipe.
Chop carrots and celery into large chunks. Slice the onion into thick slices and slice the whole garlic bulb in half lengthwise.
Preheat the oven to 450° F and remove an oven rack if needed so the roasting pan fits safely.
In a small bowl, mix paprika, poultry herbs, salt, and black pepper.
Melt the butter and mix it with the olive oil, then stir in the spice mixture.
Place the thawed turkey in a roasting pan, tuck the wings under the bird, and tie the legs together.
Place the sliced onion, halved garlic bulb, and lemon in the cavity of the bird; arrange the remaining onion, carrots, and celery around the turkey in the pan.
Pour the butter-and-oil spice mixture over the skin and rub or brush it all over the bird.
Place the turkey in the oven and roast at 450° F for 20 minutes, then lower the oven to 375° F and continue roasting for 3 to 4 hours depending on the turkey size; baste every 30 minutes and cover with aluminum foil if the top browns too quickly.
Check the turkey temperature at least 40 minutes before the end of the estimated cooking time so you can adjust cooking as needed.
When the turkey is done, remove it from the oven and let it rest for 20 to 30 minutes before carving to let the juices redistribute.
Carve in this order: cut off the legs first, then the wings, then remove the breasts.
Remove remaining meat from the carcass and freeze for later, and use the carcass to make stock if desired.