Heat olive oil over medium heat in a large soup pot. Add onions and cook until clear, about six minutes. Add garlic and cook 30 seconds. Pour in tomatoes with juices and cook about three minutes to thicken and reduce liquid, stirring occasionally.
Add kidney beans, broth, water, bay leaves, and pepper. Cover, raise heat to high and bring to a boil. Uncover and add ravioli and chard. Cook four minutes and remove from heat. Remove bay leaves. Ladle into bowls and sprinkle each bowl with two teaspoons Reggiano Parmesan cheese.