Preheat the oven to 375° F. To make the meatballs, mix the ground beef, bread crumbs, water, Parmesan cheese, garlic, oregano, parsley, salt, and pepper together in a bowl. Roll into approximately 1-inch balls and place on baking sheet. Cover and refrigerate.
To make soup, heat the oil in a thick-bottomed soup pot over medium-high heat. Sauté the onions for about 10 minutes, until golden, stirring often and scraping the bottom of the pot to prevent sticking. Add the celery and sauté another 5 minutes. Add the garlic and cook another minute over low heat. Add the chicken stock and 1 teaspoon salt and bring to a boil. Add kale and Savoy cabbage, lower heat and simmer, covered, about 15 minutes.
Meanwhile, bake meatballs for about 12 minutes (they don’t brown up as much in the oven as they would sautéed in a pan, but that’s okay). Remove from the oven and add to soup, simmering about 5 minutes to meld flavors.
Taste the soup and add more salt and a few grinds of black pepper to taste. Ladle into soup bowls. Garnish with a few shavings of Parmigiano-Reggiano cheese (a vegetable peeler works great for this).