Egg drop soup is a soup from Earth. It is a Chinese dish.
When asked what he thought of his visit to Earth, Denobulan doctor Phlox believed that Human anatomy was simplistic. However, he felt that Humans made up for this with their optimism and their egg drop soup. (ENT: "Broken Bow")
Following the return from the Xindi mission, Hoshi Sato had plans to go to Madame Chang's Mandarin Cafe with Phlox so to finally sample the egg drop soup there, after having heard Phlox talk about the soup for as long as she had known him. (ENT: "Home")