Position a rack in the lower third of the oven and heat the oven to 300°F.
Put one can of tomatoes and their juices in a food processor and process until puréed. Using a spatula or the back of a ladle, press the purée through a medium-mesh sieve set over a bowl to remove the seeds. Purée and strain the other can of tomatoes.
Cut the ribs into 2 or 3 pieces so they fit in a 7- to 8-qt. Dutch oven. Heat 1/4 cup of the oil in the Dutch oven over medium-high heat. Season the ribs with kosher salt and pepper and add them to the hot oil, fatty side down. Cook until the ribs turn a light golden brown, propping them up as needed against the sides of the Dutch oven to brown them evenly, about 6 minutes. Turn the ribs over and brown them on the other side, about 2 minutes. Transfer the ribs to a large plate, discard the fat, and clean the pan with paper towels.
Heat the remaining 1/4 cup oil in the pan over medium heat. Add the onion, garlic, parsley, and red pepper flakes and cook, stirring occasionally, until the onion just begins to color, about 5 minutes. Add the sausage and cook, stirring and breaking up the sausage with a wooden spoon until it’s lightly browned, 3 to 4 minutes.
Return the ribs to the pan and stir them around with the savory base. Raise the heat to high and add the wine. Cook, stirring occasionally, until the wine is reduced approximately by half, about 5 minutes. Add the tomatoes and the diluted tomato paste. Season with 1/2 tsp. salt and 1/4 tsp. pepper. Stir until the liquid begins to simmer.
Turn off the heat, cover the pan tightly with a lid or heavy-duty aluminum foil, and put it in the oven. Simmer very gently, turning the ribs every half hour, until the sauce has a medium-thick consistency and the meat begins to fall off the bone, about 2-1/2 hours.
Remove the pan from the oven and transfer the ribs and any meat that has fallen off the bone to a cutting board. Use a ladle to skim the fat off the surface of the sauce. When the ribs are cool enough to handle, pull the meat off the ribs. Discard the bones and any fat and connective tissue. Finely chop the meat. Stir the meat back into the sauce and simmer on the stovetop over medium heat, stirring occasionally, to allow the flavors to meld and the sauce to thicken slightly, about 10 minutes. Adjust the seasoning with salt, pepper, and crushed red pepper to taste.
The last step—toss it with pasta:
Once you've made your rich ragù, all that's left is to combine it with pasta. To serve four to six people, you'll need 4 cups ragu, 1 Tbs. unsalted butter, 1 lb. dried or fresh pasta (cooked and drained), and 1/2 cup freshly grated Parmigiano-Reggiano or Pecorino Romano.
Heat the ragù (either in the Dutch oven you used to cook it or in a 12-in. skillet, if reheating) over medium-high heat. Add the butter and then pour in the pasta and Parmigiano or pecorino. Toss over medium-high heat until the pasta and sauce are well combined. Serve immediately.
Short, full-bodied dried pastas like rigatoni and orecchiette work great with ragù, because their nooks and ridges capture the sauce. If you want to use fresh pasta, a wide shape like papperdelle can stand up to a hearty sauce. And a ragù is a good excuse to cook gnocci, too.