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 cup of water and 1/2 cup tomato juice from the can. 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.
Bring a large pot of water to a boil and add the pasta. Cook according to the package instructions, drain, 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 some of the 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.