Prepare the Short Ribs: Pat the short ribs dry with paper towels, then brush with oil. Generously season with kosher salt and black pepper.

Sear the Short Ribs: In a large Dutch oven or skillet over high heat, add the short ribs in a single layer. Sear for 3-4 minutes on each side without moving, until deeply browned. Turn with tongs to sear all sides, about 12-15 minutes total. Transfer the seared ribs to the slow cooker.

Cook the Aromatics: Reduce heat to medium, then add the sliced onion, garlic, and mushrooms to the same skillet. Sauté for about 5 minutes, scraping up any browned bits from the bottom of the pan with a wooden spoon. This adds flavor to the sauce. Transfer the vegetables to the slow cooker with the short ribs.

Prepare the Sauce: In a bowl, whisk together the red wine (or beef broth) and tomato paste until smooth. Pour over the short ribs and vegetables in the slow cooker. Add the balsamic vinegar and sprigs of thyme.

Slow Cook: Cover and cook on low for 8 hours, until the short ribs are tender and falling off the bone.

Cook the Pasta: When the short ribs are almost ready, bring a large pot of salted water to a boil. Cook the pappardelle according to package directions until al dente. Drain and set aside.

Shred the Meat: Carefully remove the short ribs from the slow cooker and transfer to a cutting board. Use two forks to shred the beef, discarding any bones and excess fat. Return the shredded beef to the slow cooker, mixing it well with the sauce.

Serve: Toss the cooked pasta with the short rib sauce or serve the sauce spooned over the pasta. Garnish with fresh Parmesan and parsley.