To make the meatballs, mix the beef, onion, 1/2 of the garlic, 1/2 of the oregano, and the Parmesan, and season well with salt and pepper. Roll the mixture into about 20 bite-size meatballs.
Heat the oil in a large saucepan. Working in batches if necessary, add the meatballs and brown them all over. Transfer the meatballs to a plate when browned.
Add the remaining garlic to the pan and cook for 1 minute. Add the browned meatballs, tomatoes, stock, tomato paste, and remaining oregano. Season with salt and pepper, to taste, and simmer gently for about 15 minutes. Add the pasta and simmer until tender, for 8-10 more minutes. Taste the soup and season with more salt and pepper, if necessary, then serve garnished with Parmesan and oregano.