Place the potato into the pan of water and slowly add kosher salt as you constantly stir. Once the potato starts to rise off the bottom of the pan, you have enough salt. Remove the potato. Then add the peppercorns, garlic, bay leaves, cumin, vinegar and wine and stir. Return the meat to the pan with the skin side up. Marinate in the refrigerator for 24 hours or up to 3 to 4 weeks.
Preheat the oven to 350 degrees F.
Remove the pork from the brine and place in a 6-inch-high roasting pan. Strain the brine and set aside. Add the carrots and potatoes to the pan. Pour 2 to 3 cups brine over the meat and cover the pan with aluminum foil. Roast for 2 hours, basting every 30 minutes.
When the skin starts to separate from the pork, turn the oven to 450 degrees F and roast until the skin is crispy, another 30 minutes.