Place the garlic clove in a small pot of water and boil for 5 minutes. Keep the water at a rolling boil to soft-boil the egg (step 4).
Add the parsley, boiled garlic clove, and chicken stock to a hand blender cup (or regular blender) and blend until the parsley is finely chopped and well combined.
Transfer the blended soup to a medium-sized saucepan and bring to a gentle simmer. Taste and add salt to your preference.
Meanwhile, soft-boil the egg. (Timing will vary depending on the size of the egg; for large eggs, boil for about 6.5 minutes.) Once done, run the egg under cold water to stop the cooking.
Stir the lemon zest and juice into the soup. Feel free to use less or more than I suggested, based on your preference for lemons.
Peel the egg, slice it in half, and gently place both halves on top of the soup before serving.