Place the bread in a shallow bowl and pour the water over the bread. Allow to sit for 10 minutes. Remove the bread from the bowl, squeezing out the excess liquid. In a mixing bowl, combine the bread, meats, onions, garlic, salt, pepper, and green onions. Mix well.
Form the meat mixture into small balls, about the size of a quarter. Bring the beef stock to a simmer, add the meatballs and cook for 25 to 30 minutes. Add the pasta and Swiss chard, and continue to cook until the pasta is tender, about 6 to 8 minutes. To serve, ladle the soup into individual bowls. Garnish with the cheese.
**To test the seasoning of the mixture, bring a small pot of water to a boil. Form the mixture into a small ball and blanch in the water for 3 to 4 minutes. Remove from the water, cool slightly and taste. Adjust the seasoning accordingly.