Add the onion, carrots, celery, potatoes, corn, and 3 cups of chicken stock to a large Dutch oven. Cover the pan with a tight-fitting lid and heat on medium to bring the vegetables to a boil. Simmer for 20 minutes or until tender.
Remove the chicken from the bones and shred it into small chunks.
Add the flour (or cornstarch if making gluten-free soup) and 1/4 cup of milk to a small bowl. Stir until smooth. Add more milk if necessary. Pour the flour mixture into the rest of the milk and stir. Pour into the vegetables. Add the last 3 cups of chicken stock into the vegetables and stir. Add the butter, pepper, and salt. Cook for 10 minutes. Remove from the heat. Add the cheddar cheese and stir until melted.
Notes
Chicken Stock
Use chicken stock instead of chicken broth for a more concentrated flavor.
Gluten-Free Soup
You can make this soup gluten-free by substituting an equal amount of a gluten-free flour, such as Cup4Cup, or by using 2 tablespoons of cornstarch in place of the flour. Also, make sure to use a gluten-free chicken stock.
Thinning Soup
If the soup is too thick on the second day, add chicken stock and milk in a 2:1 ratio. For example, add 1 cup of stock and 1/2 cup of milk.