Chop in small pieces and boil until tender, about 15 minutes:
5 oz parsnips
4 oz potatoes
3 oz fennel
1 t olive oil
The puree may be made a few hours ahead and then warmed again in the microwave just before serving.
* April 2013: Using an immersion blender (see Cool Tools 3) makes the prep time shorter and the clean-up easier. The resulting puree, however, does not have as silky a texture as the puree made in a food processor.