Combine the milk, garlic, and rosemary in a 5- to 6-quart slow cooker. Season the chicken with ¾ teaspoon each salt and pepper. Add to the slow cooker. Cook on low for 6 hours or on high for 3 hours.
Transfer the chicken to a cutting board and discard the skin and bones. Shred the meat. Skim off and discard the fat and foam from the sauce. Season the sauce with ¼ teaspoon each salt and pepper.
Toss the escarole with the oil, lemon juice, Parmesan, and ¼ teaspoon each salt and pepper. Serve with the chicken, sauce, bread, and parsley.
* Total Time: 3 hours, 15 minutes to 6 hours, 15 minutes