In a large stockpot, mix the sea salt, low carb brown sweetener, and cold water. Stir until both the salt and sweetener are fully dissolved.

Place the turkey into the brine solution, ensuring it is completely submerged. Cover and refrigerate for at least 12 hours or overnight.

Preheat the oven to 350°F.

Remove the turkey from the brine, then rinse it thoroughly under cold water. Pat it dry with paper towels. Discard the brine.

Brush half of the melted butter over the entire turkey, inside and out. Season the cavity with freshly ground black pepper.

Fill the turkey cavity with one chopped onion, two chopped carrots, two chopped celery stalks, one sprig of rosemary, the lemon quarters, and the halved garlic head.

Position the turkey breast-side down on a roasting rack set inside a shallow roasting pan. Scatter the remaining onion, carrots, celery, and rosemary around the bottom of the pan along with the bay leaf.

Pour the white wine over the vegetables at the bottom of the pan.

Roast the turkey uncovered for approximately 3 ½ to 4 hours. Two-thirds of the way through cooking, carefully turn the turkey breast-side up and brush it with the remaining melted butter.

The turkey is done when the juices run clear and an instant-read thermometer inserted into the thickest part of the thigh (near the bone) registers 165°F.

Once fully cooked, remove the turkey from the oven and let it rest for 30 minutes to allow the juices to redistribute. Carve and serve on a platter with the roasted vegetables from the pan.