Classic Turkey and Rice Soup

Name: Classic Turkey and Rice Soup
Prep time: 20 min
Cook time: 1 h 25 min
Total time: 1 h 45 min
Cuisine: American
Ingredients: 1 turkey carcass; 1 large onion, halved and skin left on; 1 large carrot, roughly chopped; 1 stalk celery, roughly chopped; 1 head garlic, halved; 1 teaspoon dried rosemary; 1 teaspoon dried thyme; 2 bay leaves; salt and ground black pepper to taste; 2 quarts water, or as needed; 2 large onions, diced; 2 carrots, diced; 2 stalks celery, diced; 2 cloves garlic, minced; 1 teaspoon poultry seasoning; 1 teaspoon onion powder; 2 cups cooked rice