Heat the oil in a large Dutch oven or pot over medium-high heat. Once the oil is hot, salt both sides of each rib, then add to the pot and cook until golden brown, about 3 minutes per side. Remove to a plate.
Reduce the heat to medium. Add the garlic, carrot, celery, onion, bell pepper and 1/2 teaspoon salt, stir to combine and then partially cover with a lid. Cook, stirring frequently, until the vegetables are soft, about 6 minutes. Add the wine, bay leaves, thyme, crushed red pepper and 1/2 teaspoon salt and simmer until most of the wine has evaporated, about 2 minutes. Nestle in the browned ribs (and any accumulated juices), then add the crushed tomatoes and 1 1/2 cups of water (it's nice to rinse the tomato can out with water and then use 1 1/2 cups of that "tomato water"). Bring to a high simmer, then adjust to a low simmer and cover the pot partially with the lid. Cook, stirring occasionally, until the meat is tender and falling apart and the sauce has reduced, about 2 hours. Be sure to scrape down the sides of the pot and add back into the sauce. Remove the pieces of pork and let them cool slightly; finely shred the meat, then stir back into the sauce. The sauce can now be finished and served or it can be cooled down, refrigerated and reheated the next day.
Bring a large pot of salted water to a boil and add the pasta. Cook according to the package instructions, reserving about 1 cup of the cooking water.
Stir the parsley into the sauce and adjust the seasoning to taste with salt. Thin out with a little of the reserved pasta water and stir in the torn basil. Divide the cooked pasta among bowls and top each with some ragout. Drizzle each bowl with a little olive oil, top with a generous amount of Parmesan and garnish with a few basil leaves.
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