Stir 3 gallons water and salt in large pot until salt dissolves. Stir in peppercorns and next 4 ingredients.
Add turkey to brine.
Place large plate atop turkey to submerge.
Place in refrigerator. Soak turkey 8 to 10 hours.
Remove turkey from brine; rinse and pat dry. (Can be prepared 1 day ahead. Store uncovered in refrigerator.)
Preheat oven to 450°F.
Place turkey on rack in large roasting pan. Rub butter over turkey.
Sprinkle with salt and pepper.
Place turkey in oven. Reduce temperature to 325°F. Roast turkey until thermometer inserted into thickest part of thigh registers 175°F, about 2 1/2 hours.
Transfer turkey to platter; tent with foil.
Let stand at room temperature 30 minutes before carving (internal temperature will rise 5 to 10 degrees).
Spoon off fat from drippings in pan, reserving 1/4 cup fat. Measure 2/3 cup pan juices. Melt butter and reserved 1/4 cup fat in heavy large saucepan over medium heat.
Mix in flour. Stir until light brown, about 2 minutes. Gradually add chicken broth, pear juice, and 2/3 cup pan juices. Simmer until thickened, stirring frequently, about 10 minutes. Stir in rum. Season with salt and pepper.
Sprinkle turkey with marjoram; serve with gravy.
No room in the fridge to brine a turkey? No problem. Put a turkey-sized oven bag in a large cooler, then place the turkey in the bag.
Pour in the brine and seal tightly.
Place ice over and around turkey, close the lid tightly, and let it brine 8 to 10 hours, adding ice periodically to keep temperature at 40° or below.
