How to Make It
Stir together 2 gallons warm water, vinegar, salt, brown sugar, peppercorns, bay leaves, and parsley stems in a 14-quart stockpot until sugar and salt dissolve, about 1 minute and 30 seconds. Let brine cool to room temperature, about 30 minutes.
Place turkey in brine, cover, and refrigerate 12 to 24 hours. Remove turkey from brine; discard brine. Pat turkey dry with paper towels. Preheat oven to 350°F. Stir together butter, parsley, thyme, lemon zest, 1 1/2 teaspoons salt, and 1 teaspoon pepper in a medium bowl until combined. Using your fingers, loosen and lift skin from turkey breast and thighs without totally detaching skin; spread some of the butter mixture under skin. Carefully replace skin, and spread remaining butter mixture over skin of breast and thighs. Drizzle turkey with 2 tablespoons oil, and sprinkle with remaining 1/2 teaspoon salt and remaining 1/2 teaspoon pepper. Place turkey, breast side up, on a wire rack in a roasting pan. Toss together carrots, celery, onion, and remaining 1/4 cup oil in a large bowl; scatter vegetable mixture around turkey in roasting pan. Stuff turkey cavity with lemon halves, dried mushrooms, shallots, garlic, rosemary, sage, and marjoram. Tie legs together with kitchen twine; tuck wing tips under.
Roast turkey in preheated oven until golden brown and an instant-read thermometer inserted in thickest part of thigh registers 155°F, about 2 hours. Transfer turkey to a carving board; remove rack from roasting pan. Let turkey rest until thermometer registers 165°F, about 30 minutes. Scoop out herb-and-mushroom mixture from inside of turkey, and add to roasting pan with vegetables. Set roasting pan on stovetop over medium-high; stir in 2 cups water, and simmer, scraping up browned bits from bottom of pan, 10 minutes. Remove from heat. Pour mixture through a fine wire-mesh strainer over a bowl; discard solids. Carve turkey, and serve with gravy.