Heat the olive oil in a large skillet over medium-high heat. Brown the lamb shoulder pieces on all sides, working in batches if needed, then transfer them to the slow cooker.
Add the diced onion, minced garlic, rosemary, thyme, and sun-dried tomatoes to the slow cooker.
Pour in the beef broth and stir in the drained white beans.
Cover and cook on low for 7 to 8 hours, until the lamb is very tender.
Stir in the chopped kale and heavy cream. Cover again and cook for 20 to 30 minutes more, until the kale softens.
Stir in the grated Parmesan cheese. Taste and season with salt and black pepper as needed before serving.