Create the Creamy Base : Pour one can of the rinsed and drained cannellini beans into the slow cooker insert. Add ½ cup of the chicken broth and mash the beans with a fork or potato masher directly in the pot until they form a coarse, creamy paste.
Build the Flavor Foundation : To the mashed beans, add the remaining two cans of whole cannellini beans, the chopped onion, sliced carrots, minced garlic, dried thyme, and minced rosemary. Stir gently to combine.
Layer the Chicken & Broth : Arrange the chicken thighs in a single layer over the vegetable mixture. Place the Parmesan rind in the center. Pour the remaining 3½ cups of chicken broth over everything.
Slow-Cook to Perfection : Secure the lid and cook on LOW for 5 to 6 hours or on HIGH for 3 to 4 hours. The soup is ready when the vegetables are tender and the chicken is fully cooked (reaches an internal temperature of 165°F / 74°C) and shreds easily with a fork.
Shred the Chicken & Wilt the Greens : Carefully transfer the cooked chicken thighs to a cutting board or bowl. Using two forks, shred the meat into bite-sized pieces. Stir the chopped kale into the hot soup in the slow cooker. Cover the pot and let the kale wilt in the residual heat for 5 to 7 minutes.
Final Assembly : Return the shredded chicken to the slow cooker. Squeeze in 1 tablespoon of fresh lemon juice and stir in the black pepper and the remaining ½ teaspoon of kosher salt. Taste and adjust seasoning if needed. Fish out and discard the Parmesan rind before serving.
Garnish and Serve : Ladle the hot soup into six bowls. Drizzle each serving with olive oil and generously sprinkle with grated Parmesan cheese and fresh parsley.