Whisk together the eggs, cheese, bread crumbs, lemon zest, and salt in a medium bowl. Be sure the eggs are evenly blended into the mixture.
Bring the broth to a simmer in a pot over medium-high heat. Pour in the egg mixture and whisk (straccia) well so that the eggs separate into small pieces and shreds, about 1 minute.
Serve the soup immediately in heated soup plates or bowls.