Trim the short ribs of excess fat. Pat the meat dry with paper towels to remove excess moisture.
In a Dutch oven, heat 1 tablespoon oil over medium heat. Add prosciutto (2 ounces), and brown, stirring often, for 2-3 minutes. Remove browned prosciutto to a plate.
Add more oil, start with 2 tablespoon, to the Dutch oven and brown the short ribs, in batches, on all sides, about 12 minutes per batch. Don't crowd the pan while browning. You should be able to see some of the bottom of the pan and there should be air space between the ribs. Removed browned ribs to a plate. Add more oil, as necessary, between batches.
If there aren't 2 tablespoons of oil in the Dutch oven, add enough oil to reach that amount. Stir in the onion (1 large), carrot (1 large), celery (2 sticks), garlic (4 cloves), allspice (1/4 teaspoon), smoked paprika (1 teaspoon), dried thyme (1 1/2 teaspoon), tomato paste (2 tablespoons), and anchovy paste (1 tablespoon). Stir often, and adjust the heat so the tomato paste and spices do not burn. Cook until vegetables are soft, about 10 minutes.
Pour the red wine (2 cups) into the Dutch oven and stir, digging down to the bottom of the pot, and scraping up all the brown bits. Continue to cook until the wine is reduced by half.
Bring 1/2 cup water to a boil. Pour it into a small bowl and add beef flavored Better than Bouillon (1 heaping tablespoon) and stir with a fork until completely dissolved and there are no lumps.
Add tomatoes with their liquid (1 can) and crush. Add bay leaves (2).
Return the short ribs and any juices that have accumulated and prosciutto to the Dutch oven, add 2 teaspoon salt and 1 teaspoon pepper, and stir well. Add just enough beef stock to cover the ribs (we used 4 cups). Bring to a boil. Immediately reduce heat and simmer. Cover the pot partially with a lid.
Stir the mixture occasionally while simmering. Cook until the meat is very tender, about 3 hours.
Remove the Dutch oven from the heat. Transfer the short ribs to a cutting board. Remove meat from the bones and shred or cut into bite-size-pieces.
Remove and discard the bay leaf. Return the meat to the pot. If fat has accumulated on top surface, skim it off the top with a large spoon and discard.
Taste the sauce and adjust the seasoning, if needed, with salt and pepper. Add the meat to the sauce in the Dutch oven and rewarm over medium-low heat.
When the sauce is almost done, cook the pasta (16 ounces) according to package instructions. Drain. Dry out pot pasta was cooked in.
When pasta is drained return it to the empty pasta pot. Spoon the warm sauce over pasta and toss to coat evenly. Portion into individual pasta bowls, top with parmesan and basil and serve.