Heat the olive oil in a large pot over medium-high heat. Add the onion and carrots and cook, stirring, until slightly softened, about 4 minutes. Add half of the garlic and 1 teaspoon each Worcestershire sauce and sage; cook 1 minute. Add the chicken broth, 3 cups water and the parmesan rind and bring to a boil. Cover, reduce the heat to medium and simmer until the vegetables are tender, about 7 minutes.
Meanwhile, mix the pork, breadcrumbs, 1 tablespoon grated parmesan, the remaining garlic and the remaining 1 teaspoon each Worcestershire sauce and sage in a bowl. Form into 1-inch meatballs.
Increase the heat to medium high and bring the soup to a boil. Stir in the orzo and cook 6 minutes. Add the meatballs and cook until they are firm and float to the top, about 4 more minutes. Stir in the spinach and cook until wilted, about 1 more minute. Ladle the soup into bowls and top with parmesan.