Place the short ribs on a sheet pan lined with a wire rack. Generously season all sides with salt and refrigerate uncovered for 1 hour to overnight. 30 minutes before cooking, remove the short ribs from the fridge and let them come to room temperature.
Preheat a Dutch oven or sauté pan over med-high heat. Add the olive oil and heat until shimmering. Carefully add the short ribs to the pan and cook, undisturbed, until browned, around 4 minutes. Flip and repeat until browned on all sides, around 8 more minutes. Transfer the browned short ribs to a tray and set aside.
Discard all but 2 tablespoons of rendered fat in the pan. Add the celery, carrot and onion and season with a pinch of salt. Cook, stirring and lifting any brown bits off the bottom of the pan, until the onions are soft and translucent, around 10 minutes. Add the garlic and cook, stirring, until fragrant, around 1 minute.
Add the tomato passata, thyme, rosemary, bay leaves and ½ teaspoon black pepper and stir to combine. Nestle the browned short ribs in the sauce. If necessary, add water until the meat is just barely submerged. Bring the sauce to a simmer, reduce the heat to low, cover with a lid and cook, stirring occasionally to prevent burning, until the meat is fall-apart tender, around 3 hours. Alternatively, transfer the pot to a 350F oven and cook until the meat is fall-apart tender, around 3 hours. If the sauce dries out, add more water to reconstitute.
Transfer the short ribs to a plate and let them cool to the touch before shredding the meat apart into thin strands. Discard the bones, thyme stems, rosemary stems and bay leaves. Return the shredded meat to the sauce along with the basil, if using, and stir through to combine. Taste the ragu for seasoning and adjust with salt and pepper as desired.
Meanwhile, bring a pot of water to a boil. Season the water generously with a big pinch of salt, add the pasta and cook it according to package instructions or until al dente. Reserve 1 cup of pasta water and drain the remaining liquid.
Add 3 cups of ragu to the pasta and stir to combine. Add the reserved pasta water and stir well to incorporate. Ladle the pasta into individual serving bowls and garnish with freshly-grated Parmigiano Reggiano, if using.