Remove the sausages from their casings (just make a slit on one end and sort of squeeze the meat out). Cook the sausage in a large pot over medium heat, breaking it up with a wooden spoon so it resembles ground beef. Cook for 10 minutes or so until cooked through and no pink remains. Remove the sausage from the pot with a slotted spoon onto a paper-toweled lined plate. Set aside. Pour out all but a tablespoon of sausage grease from the pot.
Add the onion to the pot and saute for 3 to 4 minutes, stirring frequently. Add the garlic, stirring for a minute or so until it is softened and fragrant (do not let brown). Add the tomatoes, crushing with the back of a spoon. (WARNING: this can be messy, as the tomatoes tend to squirt, so wear an apron! For a cleaner preparation, pour the tomatoes into a bowl in advance and crush the whole tomatoes with your hands. Then pour the mixture, liquid and all, into the pot.)
Let the mixture come to a boil; reduce the heat and let simmer, covered, for 20-25 minutes. Check periodically and if it seems dry, add some water.
Stir in the sausage, Balsamic vinegar, and basil and let cook for a minute or two over low heat. Remove from the heat, season with salt and pepper. This is delicious with polenta or any type of pasta.
Bring the water and salt to a boil in a medium saucepan. Once the mixture is boiling, slowing add the polenta in a steady stream, whisking constantly. Whisk for 2 minutes then reduce heat. Cover and simmer for about 30 minutes, whisking every 10 minutes or so. The mixture should be thick and creamy, sort of like grits (if you’re from the South you know what I mean!). Remove from the heat and whisk in the olive oil and Parmesan. Taste and add a little salt if you need to. Serve immediately.
*If you have leftover polenta and try to reheat it the next day, you will notice that it is very stiff–almost congealed. You can either a) cut it into little wedges and fry them up for some delicious polenta fritters OR b) put the cold polenta in a pot and a little boiling water (start with 1/4 cup and add more if you need to). Whisk the mixture together over medium heat until it reaches the desired consistency.