Heat the olive oil in a large skillet over medium-high heat. Add the lamb pieces and brown them on all sides, about 5 minutes total. Transfer the lamb to the slow cooker.
Add the onion, carrots, and garlic to the same skillet. Cook for 3 minutes, stirring occasionally, then transfer everything to the slow cooker.
Add the cannellini beans, diced tomatoes, beef broth, thyme, rosemary, bay leaves, salt, and black pepper to the slow cooker. Stir to combine.
Cover and cook on low for 7 to 8 hours, until the lamb is tender.
Remove the bay leaves. Stir in the chopped parsley just before serving.