Arrange the whole chicken, chicken feet, and optional chicken heads in the base of a 6-quart slow cooker.
Scatter the chopped celeriac, carrots, and bay leaves around the chicken pieces.
Pour all 16 cups of water into the slow cooker, ensuring the ingredients are fully covered.
Secure the lid and set the slow cooker to the low setting. Let the broth simmer gently for 24 hours without stirring.
About 30 minutes before the cooking time ends, stir in the fresh parsley and salt, adjusting the seasoning if needed.
After cooking, carefully pour the contents through a fine-mesh strainer to separate the liquid from the solids. Discard the solids unless you plan to reuse any bones for a secondary stock.
If desired, taste the broth and add more salt to your preference. Allow the broth to cool.
Once cooled, transfer the broth into clean glass jars and secure the lids.
Refrigerate for up to 7 days or freeze for long-term storage, up to 1 year.