Heat a large soup pot over medium-high heat. Add the olive oil and heat. When the oil is hot, add the pork and saute. When slightly brown, turn over and stir with a wooden spoon. Allow to cook for another 2 minutes, until evenly browned on all sides. Remove the pork and allow to cool in bowl, set aside.
In same soup pot that pork was cooked in, add minced carrot, celery, onion, and garlic. Add a pinch of salt and saute vegetables to a light brown. Add rosemary and stir. Add the caramelized pork back to the vegetables in the pot and stir. Add chianti to pot, stir and bring to boil. Add the tomato paste and the chopped tomatoes. Stir and simmer for 2 hours, skimming the top occasionally of scum that forms.