Make the brine: In a large stockpot, stir together the sea salt, brown sugar, and cold water until dissolved.
Brine the turkey: Submerge turkey in brine. Cover and refrigerate 12 hours or overnight. (Add more cold water if needed to fully cover the turkey.)
Preheat oven: Heat oven to 350°F (175°C).
Rinse and dry: Remove turkey from brine, rinse under cold water, and pat dry well. Discard brine.
Butter and season: Brush turkey inside and out with half the melted butter. Season cavity with black pepper.
Fill cavity: Add 1 chopped onion, 2 chopped carrots, 2 chopped celery stalks, 1 rosemary sprig, lemon quarters, and halved garlic to the cavity.
Set up pan: Place turkey breast-side down on a rack in a roasting pan. Scatter remaining onion, carrots, celery, and rosemary in the pan, add bay leaf, and pour wine over the vegetables.
Roast: Roast uncovered for 3 1/2 to 4 hours. About two-thirds through, carefully turn turkey breast-side up and brush with remaining melted butter.
Check doneness: Turkey is done when an instant-read thermometer in the thickest part of the thigh (near bone) reads 165°F (74°C).
Rest: Remove turkey and rest 30 minutes before carving.
Serve: Carve and serve with roasted vegetables.