Heat the olive oil in a large, heavy pot. Take care not to overheat or burn the oil. Sprinkle the chuck and pork liberally with salt and pepper. Once the oil is hot, drop in the meat and sear until brown on all sides. Remove the meat and set aside.
Add the tomatoes along with the juices from the cans. Lower the heat and slowly cook the tomatoes, breaking up into small pieces using a large spoon. Continue to cut the large pieces as the tomatoes cook; cutting them will become easier. Peel the garlic and remove the ends. Crush with the blade of a large chef's knife and drop into the sauce. Don't worry about the garlic pieces being too large; they, too, will break down as they cook. Return the meat to the sauce and continue cooking until the sauce has a chunky, but uniform consistency, 2 to 3 hours.
Add the tomato paste, 1/2 can at a time, to somewhat thicken the sauce. Simmer until desired consistency, and then stir in the basil and cook for another few minutes before serving over hot pasta (any shape will do!). This is a fresh, but hearty sauce, and every serving should have a small piece of meat served on the plate. Garnish with your favorite grated cheese and enjoy.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.