In a soup pot over high heat, bring chicken broth to a boil. Season to taste with salt and reduce heat to a simmer. Crack eggs into a medium-size bowl and beat lightly with a wire whisk. Whisk in about 1/2 teaspoon of grated nutmeg, the lemon zest, a large pinch of salt, several twists of the pepper mill and 1 3/4 ounces grated Parmesan. Pour egg mixture into simmering chicken broth and stir gently until mixture forms little rags. Simmer for another minute or so. Ladle the soup into individual bowls and sprinkle parsley over each serving. Pass more grated Parmesan separately.