Season pork with salt and pepper. Heat oil in a large, heavy pot over a medium heat. Cook the pork for 10-12 minutes, turning often until evenly browned. Transfer to a plate.
Add the onion and garlic to the pot and cook for 8-10 minutes, stirring occasionally, until the onion is starting to brown and caramelize. Add the carrot, celery, Balsamic Vinegar and tomato paste and cook, stirring occasionally, until slightly darkened in color.
Add wine and cook for 5 minutes or until the liquid is reduced by about half.
Add the stock, tomatoes, thyme, rosemary, bay leaves and the pork with any juices; season with salt and pepper and bring to the boil before reducing the heat and simmering, partially covered, until pork is fall-apart tender and the sauce is thickened. This should take approximately 2½ hours.
Bring 6 cups salted water to a boil in a large pot. Whisking constantly, gradually add polenta; reduce heat to medium-low. Cook, whisking often, until polenta is tender and creamy, about 20–25 minutes (if polenta becomes too thick too soon, loosen mixture by adding more water and continue cooking).
Add butter and ½ cup Parmesan to polenta and whisk until melted; season with salt and pepper and spoon into bowls and top with the pork that you have shredded slightly using two forks. Scatter parsley and more Parmesan over the top.