In a large pot, combine the Parmesan rind with the stock, garlic and a generous pinch of salt. Bring to a boil over high heat, then cover and let simmer over low heat.
Meanwhile, in a large bowl, combine the pork with the breadcrumbs, egg, dill, 1/4 cup finely grated Parmesan, 1 1/2 teaspoons salt and 3/4 teaspoon pepper; mix well. Gradually mix in 1/4 cup of the Parmesan broth, then form the mixture into 16 meatballs.
In a large skillet, melt the butter in 1 tablespoon of the olive oil over medium heat. Working over a bowl, break any long pasta into small pieces. Add all the pasta to the skillet and cook, stirring, until browned all over, about 5 minutes. Add the pasta to the Parmesan broth.
Wipe out the skillet and heat the remaining 2 tablespoons olive oil over medium heat. Add the meatballs and cook, turning occasionally, until browned all over, 5 to 7 minutes. Add the meatballs to the Parmesan broth, cover and simmer until the meatballs are cooked through, 5 to 7 minutes. Stir in the spinach and peas and simmer until warm, 3 minutes. Serve in bowls, topped with grated Parmesan, dill sprigs and black pepper.