Season the short rib chunks generously with salt and pepper. Heat olive oil in a large skillet over medium-high heat and brown the meat in batches. Don’t overcrowd the pan or you’ll steam instead of sear—that’s not the vibe here.
Add onion and garlic; sauté until translucent and fragrant, about 3–4 minutes. Scrape up any browned bits from the bottom of the pan for flavor glory.
Pour in beef broth and bring to a simmer. Let it cook gently for about 20 minutes, until the meat is tender and starting to shred. If you’re feeling fancy, skim off some fat, but not all—fat = flavor.
Stir in heavy cream and Parmesan. Simmer until the sauce thickens to cling-to-pasta consistency, about 5–7 minutes. If it’s too thick, splash in a little more broth or water.
Meanwhile, cook the pasta in salted water until al dente. Reserve a splash of the cooking water.
Shred the meat into bite-sized pieces and return it to the sauce. Stir in Dijon mustard if using. Toss the pasta into the skillet with sauce, adding a splash of reserved pasta water to loosen if needed.
Serve hot, garnished with parsley or chives. Optionally sprinkle extra Parmesan on top. Enjoy the oohs and aahs from everyone at the table.