Combine flour, grated Parmesan cheese, salt, freshly grated nutmeg in a large bowl. Stir in the lightly beaten eggs. Cut the butter in small pieces and add to the mixture. Wet a cloth napkin, squeeze out, and spread it out flat. Spoon the cheese mixture into the middle of napkin, bring up the ends of the napkin, and tie together to form a tight bag. Place the bag into a soup kettle with the 10 cups of Chicken and Beef broth. Bring to boil, cover, simmer for 2 hours.
Remove the bag from the broth. Let it cool to room temperature. Untie the bag, remove the now-hardened mixture from the napkin, and cut into 1/2 inch slices. Cut these slices into cubes. Reheat the broth, add the cubes, and continue to boil for 10 minutes. Serve piping hot.