Put the loin in a large zip-top bag, pour in the brine, seal well, and place in a large bowl.
Cure in the refrigerator for 72 hours, turning the bag once every 24 hours.
Drain the loin in a colander or large basin and rinse well with cold water. Blot it dry with paper towels. Place the loin on a wire rack over a rimmed baking sheet in the refrigerator or in a cool place in front of a fan (the goal is to create good airflow), and let it dry until the surface feels papery and tacky, at least 4 hours, or overnight.
Put the cornmeal on a large plate and roll the loin in the cornmeal to coat evenly. Wrap tightly in plastic wrap until ready to eat.
To serve, heat