Heat oven to 350°F. Using a very sharp knife, carefully split pork belly crosswise in half. Season both sides of both pieces with salt and pepper.
Heat 2 tablespoons clarified butter in a large heavy skillet or 6-quart braising pan. Add one pork belly piece, fat side down. Cook until fat is nicely brown, about 3 to 5 minutes. Turn pork belly piece over and brown the other side. Transfer pork belly to a plate; discard fat in skillet or pan. Repeat browning with remaining 2 tablespoons clarified butter and pork belly piece. Discard fat from skillet or pan.
With skillet or braising pan away from heat, add 1/3 cup wine. Return skillet or pan to heat and cook over low heat, scraping brown bots from bottom of pan; remove from heat. If using braising pan, return pork belly pieces to pan. If using skillet, pour liquid from skillet into a 6-quart Dutch oven and add pork. To the pork, add remaining wine, stock, onion, celery, carrot, and thyme. Bring to boil and cover tightly.
Bake in preheated oven for 3 1/2 to 4 hours. Remove and let pork belly cool completely. Reserve braising liquid.
Portion pork belly into 3 ounce to 4 ounce rectangle pieces. Place belly pieces in a large skillet or braising pan with enough braising liquid to cover.
Reheat on stove top over medium heat for 5 to 10 minutes or until the internal temperature reaches 155°F.
To make grits: Bring heavy cream and water to a boil in a large, heavy saucepan. Reduce heat to medium-low. slowly stir in grits. Cook over medium-low heat for 5 to 10 minutes until fully cooked. Stir in salt and pepper.