Preheat your oven to 300°F.
In a large cast iron pot or Dutch oven, heat a drizzle of oil over medium-high heat. Season the short ribs generously with kosher salt. Sear on all sides until deeply browned. Remove and set aside.
In the same pot, add the vegetables and sauté until slightly softened and reduced in size, scraping up any browned bits from the bottom.
Stir in the tomato paste and cook for a minute until it darkens slightly. Pour in the wine, scraping the bottom of the pot to release all the flavorful bits. Add the crushed tomatoes, beef broth, rosemary, and bay leaf.
Return the short ribs to the pot. Cover and transfer to the oven. Cook for 2–3 hours, until the meat is very tender and falling off the bone.
Remove the ribs from the sauce and discard the bay leaves and rosemary. Remove the bones and shred the meat. Return the shredded meat to the sauce.
Toss the sauce with cooked pasta until fully coated. Serve hot, with extra sauce spooned over the top.