An overnight wet brine infuses and plumps up the meat so it stays moist. Line a roasting pan with the brining bag before adding the liquid and the turkey so everything stays in place.
To prepare brine, bring 2 cups cider, sugar, 1/2 cup salt, and peppercorns to a simmer in a large saucepan over medium-high. Cook 5 minutes or until salt and sugar dissolve. Remove pan from heat. Stir in remaining 4 cups cider, garlic, bay leaves, and 2 onions. Cool completely. Combine brine with 6 cups water in a brining bag.
To prepare the turkey, remove giblets and neck; discard. Add turkey to brine. Add water to bag, 1/2 cup at a time, as needed to cover turkey. Refrigerate 12 to 24 hours.
Preheat oven to 350°F.
Remove turkey from brine; discard brine. Pat turkey dry. Combine 1/4 cup butter, chopped thyme, pepper, and 1/2 teaspoon salt in a small bowl. Starting at neck cavity, loosen skin from breast and drumsticks by inserting fingers and gently pushing between skin and meat. Rub butter mixture under loosened skin. Lift wing tips up and over back; tuck under turkey. Place 1 onion, 1 apple, 1 carrot, and 2 thyme sprigs in body cavity. Tie legs with kitchen twine.
Place turkey on the rack of a roasting pan coated with cooking spray. Place remaining onions, apples, carrots, and thyme sprigs in bottom of pan; place rack with turkey in pan. Add 2 cups cider to pan. Bake at 350°F for 1 1/2 hours.
Combine remaining 2 tablespoons butter and jelly in a small saucepan over medium-high; cook 2 minutes. Brush half of jelly mixture over turkey. Bake at 350°F for 30 minutes. Brush turkey with remaining half of jelly mixture; bake at 350°F for 30 minutes or until a thermometer inserted into the thickest part of the thigh registers 160°F.
Place turkey on a cutting board. Let stand, loosely covered with foil, 20 minutes (internal temperature will rise to 165°F). Remove skin before serving. Reserve pan drippings for gravy, if using. Serve with roasted apples and vegetables from pan.