Add the olive oil to a large, heavy-bottomed pot (I use a 5-qt Dutch oven) over medium-high heat. Use paper towel to pat the surface of the beef short ribs as dry as possible. Generously season the short ribs with 1 heaping tablespoon kosher salt and ground black pepper as desired. Once the oil in the pot is shimmering hot, carefully add in the seasoned short ribs. Work in batches, as necessary, to avoid overcrowding the pot (which prevents browning). Cook for 3-4 minutes per side, until nicely browned. Transfer the browned short ribs to a plate and set aside. Repeat, as necessary, with the remaining short ribs. Once all of the short ribs are browned, carefully drain off all but 2 tablespoons drippings from the pot. Set aside and discard once cooled. Returning the pot to medium heat.
Add the soffritto (carrots, onion, and celery) to the same pot used to brown the short ribs, seasoning with 1 teaspoon kosher salt and ground black pepper as desired. Stir to combine and cook, stirring occasionally, until the soffritto is deeply browned, 15-20 minutes.
Add the garlic to the pot with the soffritto. Stirring constantly, cook until fragrant, 1-2 minutes. Add the tomato paste to the pot, stirring to coat the soffritto. Cook 2-3 minutes, until browned.
Increasing the heat to medium-high, pour the red wine into the pot. Stir constantly, using a wooden spoon to scrape up any browned bits that may have formed at the bottom of the pot. Cook for 3-4 minutes, until the wine is almost completely absorbed into the soffritto.
Tie the herbs together using kitchen twine (or finely chop if you do not have twine), then add to the pot with the bay leaves and parmesan rind (if using). Add the crushed tomatoes, beef broth/stock (or water), and browned short ribs from Step 1. Stir to combine. Bring the mixture to a boil. Reduce heat to a low. Cover and simmer, stirring occasionally, for 2 ½ – 3 hours, or until the short ribs are fall-apart tender. If the ragu begins to reduce too much (i.e. it loses too much of its liquid too quickly), feel free to add in a splash more water and/or reduce the heat further.
Carefully transfer the short ribs to a plate or cutting board. At this point, you can remove and discard the spent herbs, bay leaves, and parmesan rind from the pot, as well. Use tongs or 2 forks to shred the short ribs into bite-sized pieces, discarding the bones as you go. Return the shredded short ribs to the pot with the ragu. Stir to combine. At this point, you can cool and store for later use (see Recipe Notes for storage and freezing directions), or proceed with making the short rib ragu pasta (below).
Bring a large pot of salted water to a boil. Add the pasta and cook, stirring occasionally, until the pasta is cooked to al dente according to package directions. Carefully dip a liquid measuring cup into the pot, reserving about 1 cup of the starchy pasta water, and set aside. Carefully drain the pasta – do NOT rinse it!
Meanwhile, as the pasta boils, bring the braised short rib ragu up to a simmer. Stir in the heavy cream and parmesan cheese. Continue to simmer over low heat, stirring occasionally.
Add the cooked pasta to the pot with the braised short rib ragu sauce, tossing to coat. The short rib ragu should evenly coat the pasta. Add in some of the reserved pasta water if the ragu needs to loosen up a little; add in an extra handful of parmesan if it needs to tighten up a little. Cook over medium heat for 1-2 minutes, allowing the pasta to meld with and absorb some of the ragu.
Portion the short rib ragu pappardelle into individual pasta bowls, topping with additional grated parmesan, chopped fresh herbs, and/or crushed red pepper as desired. Serve immediately. Enjoy!