Smoked Turkey Rice Soup

Name: Smoked Turkey Rice Soup
Prep time: 30 min
Cook time: 2 h
Total time: 2 h 30 min
Cuisine: American
Ingredients: 1 smoked turkey carcass; 1 (32 fluid ounce) container vegetable broth; 2 cups water; 2 cups chopped fresh green beans; 1.5 cups frozen corn; 1 cup shredded carrot; 1 cup white rice; 0.5 cup chopped celery, or to taste; 0.5 cup chopped onion; 0.5 cup chopped green bell pepper; 0.5 cup chopped red bell pepper; 1 (4 ounce) package cream cheese, or more to taste; 1 cup shredded Cheddar cheese, or to taste; ground black pepper to taste