Loosely wrap bay leaves, allspice berries, peppercorns and cloves in cheesecloth and tie securely with kitchen string. Place in slow cooker. Add split peas, ham, onion, celery and carrots. Stir in chicken broth.
Cover and cook on high until peas are falling apart, about 4 hours. Remove and discard cheesecloth. Stir in mint and season with salt and pepper to taste. Ladle into bowls and serve.