Brown the sausage in a skillet over medium heat, breaking it up with a spoon until no longer pink. Drain excess fat and transfer the sausage to the slow cooker.
Add the sweet potatoes, onion, garlic, cannellini beans, diced tomatoes, chicken broth, oregano, and red pepper flakes to the slow cooker. Stir to combine. Season with salt and black pepper.
Cover and cook on low for 6 hours or high for 3 hours, until the sweet potatoes are tender.
Stir in the kale and bread cubes. Cover and cook for 20 more minutes on low until the kale wilts and the bread softens into the soup.
Ladle into bowls and top each serving with grated Parmesan cheese.