Tie thyme, parsley, and bay leaves together with cooking twine to form a bouquet garni; set aside.
Place chickens, and neck and feet, if using, in a large stockpot. Add salt and 3 1/2 quarts cold water; bring to a boil over medium heat, and immediately reduce heat to a simmer, skimming off any impurities that rise to the top.
Add ice cubes and skim fat and any additional impurities that form on surface. When liquid returns to a simmer, add bouquet garni, celery, carrots, onions, and peppercorns. Continue simmering for 2 hours, skimming surface frequently.
Remove from heat and let stand 30 minutes.
Set a fine mesh strainer over a large container and ladle stock over strainer. Discard liquid at the very bottom of the stockpot, as it is likely to contain impurities. Let stock cool completely. To do so quickly, fill a sink or large bowl with ice and submerge container in ice.
Once cooled, transfer stock to refrigerator for up to 2 days or freeze.