Sauté onion in olive oil until translucent in a stock pot of sufficient size to hold all of the ingredients.
Add the garlic and saute briefly, but do not let it brown. Pour in the cans of puree, the paste, and all of the water (7 cups). Mix well.
Add the salt, pepper, sugar, and half of the basil leaves, torn.
Bring the sauce to a boil, cover and turn down to a low simmer.
Meanwhile, in a separate sauté pan, brown the ribs seasoned with salt and pepper, along with the sausage in just enough olive oil to coat the pan (1 tbsp) about 8-10 minutes. Just brown the meats. You will be cooking them in the sauce.
Add the browned meats to the sauce and simmer 1 1/2 to 2 hours, skimming off the fat that rises to the surface. When the rib meat is tender, the sauce is done.
Cook the pasta in boiling salted water until al dente. Drain and add enough sauce to amply coat along with the remaining torn basil leaves. Serve meats, extra sauce, and cheese for grating on the side.