Don't you have a dishwasher?Cleaning a microplane is like cleaning a box grater to me. Gotta be careful of the sharp edges and what direction you are going. Cheese falls right off, but zest doesn't (for me) and I end up using my fingers to scrape it from the underside.
If anything sticks underside I use a teaspoon to scrape it off. Then run it under a tap if needed and into the dishwasher.

