Heat 1 tablespoon of oil in a Dutch oven or heavy pot. While the pot is heating, in a large bowl, season the pork with the salt and pepper. Sear the pork on all sides, about a minute per side, remove from the pot and set aside.
Heat the remaining oil in the pot and then add the sausage, break up the sausage with a spatula and cook until golden brown, about 4-5 minutes.
To the pot, add the onion and carrot and cook for about 3 minutes, stirring often. Add the garlic and cook for 1 minute. Season with salt and pepper as desired and cook until the vegetables are soft, about 2 minutes.
Stir in the white wine, tomato paste, brown sugar, tomatoes, thyme, oregano, bay leaves, and cheese rind if you have that. Mix together then add the meat back to the pot and stir in. Season with additional salt and pepper to your liking.
Reduce heat to low and simmer for 3 hours, the meat should be fall apart tender and the sauce slightly thickened. Use two forks and shred the pork and stir into the sauce.