Unlike the Asian soup with a similar name, this soup contains small specks of cooked egg rather than ribbons of egg. The eggs look like straccetti, or "little rags," which explains the actual Italian name of the soup, stracciatella (straht-chee-ah-TEHL-lah) alla Romana.
Combine 1 cup broth, grated cheese, and next 3 ingredients in a medium bowl; stir with a whisk until eggs are lightly beaten.
Bring remaining broth to a boil in a Dutch oven over medium-high heat. Reduce heat to low; gradually pour egg mixture into broth, stirring constantly with whisk (the faster you stir, the finer the pieces of egg). Cook 3 minutes, stirring constantly. Remove from heat; stir in pepper, salt, and nutmeg. Serve immediately.