Place chicken thighs in a 4- to 5-quart slow cooker. For bouquet garni, cut an 8-inch square from a double thickness of 100 percent cotton cheesecloth. Place thyme sprigs, parsley stems, bay leaves, garlic, and peppercorns in the center of the cheesecloth square. Bring up corners of the cheesecloth and tie with 100 percent cotton kitchen string. Add bouquet garni to slow cooker. Pour broth over all.
Cover and cook on low-heat setting for 7 to 8 hours or on high-heat setting for 3-1/2 to 4 hours. Remove bouquet garni and discard.
Using a slotted spoon, transfer chicken to a large bowl. When chicken is cool enough to handle, remove meat from bones. Using two forks, shred meat. Add enough of the cooking juices to moisten meat. Strain and reserve cooking juices to use for chicken stock. Place 2-cup portions of chicken and chicken stock in separate airtight containers and refrigerate for up to 3 days or freeze for up to 3 months. Makes 6 cups.