Soften the vegetables. Heat the olive oil in a frying pan over medium heat. Add the onion and garlic and cook gently until softened and translucent. Add the leek and celery and continue cooking until softened, without browning.
Fill the slow cooker. Transfer the softened vegetables to the slow cooker. Add the rinsed red lentils, carrots and bay leaves.
Add the gammon and stock. Place the smoked gammon joint on top of the lentils and vegetables. Pour in the stock, ensuring the gammon is just covered.
Slow cook. Cover and cook on high for 3–4 hours or on low for 5–6 hours, until the gammon is cooked through and tender and the lentils and vegetables are soft.
Shred the ham. Carefully lift the gammon out of the slow cooker and leave it to rest on a chopping board for a few minutes. Remove any rind and excess fat, then shred the meat with two forks, leaving some larger pieces for texture.
Thicken the soup. Remove the bay leaves. Use a stick blender to blend a portion of the lentils and vegetables directly in the slow cooker, leaving plenty of texture in the remaining soup.
Add the greens. Stir in the chopped cavolo nero or kale. Cover and allow it to wilt in the hot soup for about 5–8 minutes, until tender.
Finish and serve. Return the shredded ham to the slow cooker and stir well. Taste before adding any salt, as the smoked gammon will already have seasoned the broth. Add a little hot water or stock if the soup is too thick, then serve.