In a food processor, grind pork liver until smooth, about 10 seconds. Add butter and egg. Pulse to combine. Transfer pork mixture to a medium bowl. With rubber spatula, mix garlic, bread crumbs, salt, marjoram and pepper until well combined. Refrigerate pork mixture for 30 minutes. (This allows the mixture to become stiff so no more bread is needed.) Meanwhile, bring beef broth to a boil over high heat in a large saucepan. Adjust heat to medium-high and simmer broth. Using a metal soup spoon, scoop out one heaping portion of liver mixture from bowl. Use another spoon to scrape liver mixture into broth, forming an oval-shaped dumpling. Cook the pork dumplings in the simmering broth, stirring occasionally, for 5 minutes. Add pasta. Continue simmering, stirring occasionally, until dumplings are cooked through and pasta is soft, about 15 minutes. Season with more salt and pepper if necessary. Serve into small bowls.