Heat the olive oil in a large Dutch oven over medium heat. Add the lamb pieces and brown them on all sides, about 6 to 8 minutes total. Remove the lamb to a plate and set aside.
Add the onion, carrots, and garlic to the same pot. Cook for 5 minutes until the onion softens and the garlic smells fragrant.
Pour in the Sangiovese wine and scrape the bottom of the pot to loosen any browned bits. Let the wine simmer for 3 minutes to reduce slightly.
Return the lamb to the pot along with the broth, rosemary, salt, and pepper. Bring everything to a boil, then lower the heat to a gentle simmer. Cover and cook for 1 hour and 15 minutes.
Stir in the cannellini beans and chopped kale. Simmer uncovered for another 15 minutes until the kale wilts and the beans warm through.