Cook the sausages: Heat a large cast-iron or stainless steel skillet over high heat. When the skillet is hot, use a pair of metal tongs to arrange the sausages in a single layer. (There is no need for oil as the sausages will soon start to render their grease.) Turn the heat to medium and brown the sausages on all sides, taking care that they are cooked through, 8 to 10 minutes total. Remove the sausages to a medium bowl. Pour off the grease and add the wine, simmering over medium heat to reduce to about 1/4 cup liquid, 2 to 3 minutes. Pour the reduced wine over the sausages and wipe the skillet clean.
Cook the pork chops: Add the canola oil to the same skillet. Sprinkle the pork chops on all sides with salt. When the oil begins to smoke lightly, add the pork chops in a single layer and brown on all sides over medium heat, 5 to 8 minutes total. Remove the pork chops to the bowl with the sausages. Leave the grease in the skillet.
Make the sauce: Stir the onions and garlic into the same skillet and cook over medium-low heat until translucent, 8 to 10 minutes. Sprinkle with salt. Stir in the canned and cherry tomatoes with 1/2 cup water and simmer gently until the sauce is somewhat thick and tasty, 20 to 25 minutes. Stir the sausages and pork (and any meat juices) back into the sauce and bring to a simmer over medium heat. Simmer 2 to 3 minutes. Turn off the heat, then stir in the cheese, red wine vinegar and basil leaves. Taste for seasoning.
Cook the pasta: Bring 6 quarts of water to a rolling boil in a large pot. Add a generous handful of salt and bring the water back to a boil. Taste the water. It should be salty like seawater. Add the pasta and stir with a large slotted spoon to ensure the pasta does not stick as it cooks. Cook until still quite firm, 8 to 10 minutes. Drain.
Finish the dish: Spoon the meat over the pasta in individual bowls or serve in a large bowl, family style. You can also just leave the pot of meat and sauce and the pasta separate and let people serve themselves.