Rinse the chicken carcass under cold water to remove any residue.
Peel and chop the carrot, dice the onion, chop the celery, and halve the garlic cloves.
Place the chicken carcass in the slow cooker. Add the carrot, onion, celery, garlic, parsley, apple cider vinegar, salt, and water.
Set the slow cooker to low heat. Cover and cook for at least 12 hours (up to 24 hours for a richer broth).
Carefully strain the broth into a large bowl or pot using a strainer or mesh sack. Discard the solids (vegetables and bones).
Allow the broth to cool to room temperature. Once cool, refrigerate until a layer of fat forms on top. Remove the fat layer and discard or save it for cooking.
Notes
Leftovers: Refrigerate in an airtight container for up to four days. Freeze for up to three months.