Heat oil in a heavy large Dutch oven or soup pot over medium-high heat. Add apples, parsnips, onion and coriander and sauté until slightly softened, about 12 minutes. Add 4 cups broth and bring to boil. Reduce heat to medium-low, cover and simmer until apples and parsnips are tender, about 40 minutes.
Puree soup in blender in batches. Return puree to saucepan. Thin with more broth if desired. Season soup with salt and pepper. Ladle into bowls. Sprinkle with parsley; garnish with apple slices if desired and serve.
IMPORTANT! Always use great caution when pureeing hot liquids. If you have time, allow the soup to cool before blending. Never fill the container more than half full and cover the lid with a folded kitchen towel and hold it in place before you turn on the blender. The initial surge of the blender's contents can cause the lid to pop open, possibly scalding you if still hot and certainly making a mess of your kitchen.