Shred the rotisserie chicken, separating the meat from the bones and skin—set aside the good meat for later. Heat the olive oil in a large pot over medium-high heat and add the chicken bones, skin, and any smaller pieces along with 1 carrot (roughly chopped), 1 celery stalk (roughly chopped), and 2 garlic cloves (smashed). Sauté for 3 minutes to develop deeper flavor. Add 6 cups of water and 3.5 teaspoons of salt, then bring to a boil. Reduce heat and simmer for 15 minutes to extract all the chicken flavor into the broth.
Pour the broth through a fine-mesh strainer into a clean pot, discarding all solids—this clear broth is your flavorful base. While the broth finishes simmering, melt the butter in a separate pan over medium heat and add the diced large carrot with ¼ teaspoon of salt. Cook for 3-4 minutes until the carrots are just tender but still have a slight bite. I like to let the carrots soften gently in butter rather than boiling them, which keeps them bright and flavorful.
Bring a separate pot of water to a boil with 2 teaspoons of salt, then add the trimmed green beans cut into 1-inch pieces. Blanch for exactly 5 minutes to preserve their bright green color and slight crunch. While the beans cook, prepare a bowl with ice water. Once the beans are done, drain them and immediately transfer to the ice water to stop the cooking process. Drain again before adding to the soup—this technique locks in the fresh, vibrant color and texture.
Warm the strained broth from Step 1 over medium heat and add the shredded chicken meat, the butter-cooked carrots from Step 2, and the blanched green beans from Step 3. Season with ½ teaspoon of salt and ½ teaspoon of black pepper, tasting as you go. Stir in any juices that have collected from the rotisserie chicken for extra depth of flavor.
Ladle the hot soup into bowls and garnish generously with fresh chopped parsley. The parsley adds a bright, fresh finish that complements the rich, comforting broth beautifully.