Pat the beef short rib dry and season all sides thoroughly with sea salt and black pepper.
Heat the olive oil in a small heavy-bottomed pot over medium-high heat and sear the beef until a deep golden crust forms on all sides.
Remove the beef from the pot and add the diced onion and carrot, sautéing until the vegetables are softened and translucent.
Stir in the minced garlic clove and tomato paste, cooking for one minute until fragrant, then pour in the beef bone broth to deglaze the pan.
Return the beef to the pot, cover tightly with a lid, and simmer on low heat for 2 to 3 hours until the meat is fork-tender.
While the beef rests, cook the pappardelle in a pot of boiling salted water until al dente, then drain and reserve a small amount of pasta water.
Shred the braised beef using two forks, discarding any large pieces of rendered fat, and toss the meat and sauce with the cooked pasta.
In a small bowl, combine the fresh parsley, lemon zest, and the remaining minced garlic to create a fresh gremolata.
Serve the pasta in a shallow bowl topped with the zesty gremolata for a bright finish.