Prep the Chicken and Veggies: Rinse the chicken under cold water and place it in a large pot. Chop the vegetables as directed and add them to the pot, along with the garlic, thyme, and bay leaves.
Add the Broth: Pour the chicken stock or broth over the chicken and vegetables. The liquid should cover all the ingredients. If not, add enough water to just cover.
Simmer: Bring the pot to a gentle boil over medium-high heat. Once boiling, reduce the heat to low, allowing the soup to simmer uncovered for 2.5 to 3 hours. Skim off any foam that rises to the top during the first few minutes of cooking.
Check the Chicken: The soup is ready when the chicken is so tender that it falls apart at the touch. Carefully remove the chicken from the pot and let it cool enough to handle.
Shred the Chicken: Discard the skin and bones and shred the meat into bite-sized pieces. Return the chicken to the pot.
Season: Taste the soup and adjust the seasoning with kosher salt and freshly ground black pepper as needed.
Serve: Garnish each serving with minced fresh dill, parsley, or your choice of herbs.