Heat olive oil in a Dutch oven over medium-high heat. Brown the lamb shanks on all sides, then remove and set aside.
In the same pot, add the chopped onion and cook until softened. Add the garlic and cook for another minute.
Pour in the red wine and beef broth, scraping up any browned bits from the bottom of the pot. Add the rosemary sprigs, salt, and pepper.
Return the lamb shanks to the pot. Cover and transfer to the preheated oven. Braise for 2 to 2.5 hours, or until the meat is tender and falling off the bone.
Remove the rosemary sprigs before serving. Serve the lamb shanks with the braising liquid spooned over the top.