Brine: A day before serving, heat 3 quarts of water, salt and sugar in a stockpot, stirring to dissolve the sugar and salt. Remove from heat, add remaining water and stir. Cool to room temperature. Lower turkey into brine. Cover and refrigerate 12 hours or overnight.
Rub: Mix all ingredients in a bowl. Pulse mixture in a spice grinder in a few batches until finely ground. Seal in an airtight container and store in a cool, dry place for up to 2 months.
Heat oven to 325 degrees F. Drain and pat turkey very dry inside and out. Place onion, garlic and bay leaves inside the cavity. Set bird breast-side up on a roasting rack in a roasting pan. Brush with butter and spread 1/2 cup Prairie Rub over entire bird. Tent bird with aluminum foil.
Roast turkey for 2 hours. Remove foil. Increase oven temperature to 425 degrees F and continue to roast until an instant-read thermometer registers 170 degrees F in the thigh of the bird, about 30 minutes more. Remove turkey from the oven and set aside to rest 20 minutes. Before carving, remove and discard onion, garlic, herbs and bay leaves.