Melt the butter in a large pot over medium-high heat; cook the onion and garlic in the melted butter until tender, 5 to 7 minutes. Pour the beef stock into the pot; add the tomatoes, green beans, carrot, kale, Italian herbs and bay leaf. Bring the mixture to a boil.
Stir in the meatballs and tortellini; return to a boil and cook another 5 minutes. Ladle into bowls and top each with about 1 teaspoon Parmesan cheese to serve.