Prepare the vegetables. In a large pot, combine the water, bouillon cubes, carrots, basil, parsley, diced potatoes, onion, and optional green beans. Add the salt, keeping in mind that the bouillon may already contain salt.
Cook until tender. Bring the mixture to a boil, then reduce the heat and simmer until the potatoes and carrots are fork-tender, about 15–20 minutes, depending on their size.
Add the chicken and cheese. Stir in the cooked, diced chicken, shredded cheddar cheese, and cream cheese.
Prepare the milk mixture. In a separate bowl, whisk the milk and cornstarch until smooth.
Make the soup creamy. Slowly stir the milk mixture into the soup. Add the sour cream and stir to combine.
Heat gently. Cook over low heat, stirring frequently, until the cheeses have melted and the soup is heated through. Avoid boiling, as the dairy may separate.
Season and serve. Taste and add salt and pepper as needed. Serve warm.
