Heat more oil in the pot, if needed. Add the onion, carrot, and celery and cook, stirring often, until the vegetables soften, about 5 minutes. Add the garlic and cook until fragrant, about 1 minute. Add the wine and bring to a boil. Add the tomatoes and their purée, the oregano and the basil. Return the roast to the pot and bring the sauce to a boil. Reduce the heat to low and cover the pot. Simmer, occasionally turning the roast in the sauce, until the meat is fork tender, about 2 hours.
Transfer the meat to a platter. Remove the pot from the heat and let stand for 5 minutes. Skim off any fat that rises to the surface of the sauce. Carve the meat and pour the sauce on top. Serve hot.