Pat the lamb dry and season it with salt and pepper. Heat the olive oil in a Dutch oven over medium-high heat, then brown the lamb in batches until all sides are seared. Remove the lamb to a plate.
Lower the heat to medium and add the onion, garlic, and carrots to the same pot. Cook for 5 minutes, stirring often, until the onion softens.
Stir in the tomato paste and cook for 1 minute. Pour in the Chianti and scrape the bottom of the pot to loosen any browned bits.
Return the lamb to the pot along with the beef broth and rosemary sprigs. Bring the mixture to a gentle simmer, then cover and cook for 1 hour 15 minutes.
Stir in the white beans and continue simmering uncovered for 20 to 25 minutes until the lamb is fork-tender and the sauce has thickened slightly. Remove the rosemary sprigs before serving.