Add the 6 cups of broth and the lemon zest. Increase the heat to high and bring the broth to a boil. Stir in the pasta and cook for 2 minutes. Reduce the heat to low.
In a medium bowl, beat the egg yolks. Slowly add one cup of the hot broth to the yolks, whisking as you add. Then whisk the egg mixture back into the soup pot. Whisking consistently as you pour the mixture back in will allow it to fully and smoothly incorporate into the broth.
Remove soup from the heat, ladle into bowls, and garnish with the Parmesan cheese.
Notes
Use the smaller amount of pasta if you prefer a "brothier" soup, the larger amount if you like it a bit heartier.
While I started making this soup with angel hair pasta many years ago, I now often make it with rice or bean vermicelli noodles for a gluten free option. The bean vermicelli are glassier when cooked and difficult to break, so I often rough cut them with my kitchen scissors (in the pot, once cooked) to make the soup easier to eat. My kids actually love these noodles.