Preheat oven to 350 degrees and lightly grease a baking sheet.
In a medium bowl whisk together oats, flour, baking powder, baking soda, salt, cinnamon, and nutmeg.
In a large bowl cream together butter and sugars until light and fluffy (2-3 minutes.) Add eggs and vanilla and mix well.
Add dry ingredients to wet ingredients and stir until incorporated. Drop heaping tablespoons of cookie dough onto baking sheet 2-3 inches apart. Bake for 10-12 minutes until golden. Allow to cool for 5 minutes on the baking sheet, then transfer to a cooling rack.
After all of the cookies are made, whisk together the ingredients for the icing. Dip cookies in the icing and allow to cool 10-20 minutes until icing is set. Store in airtight container at room temperature for up to five days.