For the leftover roast chicken stock: Put the cleaned chicken carcass in a large saucepan along with the salt, peppercorns, celery, bay leaf, carrots and onions and cover with cold water, about 8 cups. Bring to a boil, reduce the heat to a low simmer and cook for 1 1/2 hours. Strain the stock through a fine-mesh sieve or a colander lined with paper towels. You should have 6 cups stock after cooking.
For the soup: Heat the olive oil in a large soup pot over medium-high heat until hot. Add the garlic, carrots, celery and onions and saute until tender, 4 to 5 minutes. Add the kale and cook for about 2 minutes. Season with salt and pepper. Hand-crush the canned tomatoes directly into the pot; it's nice to keep a little texture with the tomatoes. Add the chicken stock and simmer the soup on medium heat for 20 minutes. Fold in the rice and chicken and simmer for 5 more minutes. Finish with chopped parsley and serve in warm bowls with grated Parmesan on top.