Preheat oven to 350 degrees line baking sheets with parchment paper or baking mats.
Pulse the oatmeal in a food processor 10 times. (You want a variety of textures)
In a medium bowl add the pulsed oatmeal, flour, baking soda, salt, cinnamon, and nutmeg and whisk until combined.
In a large bowl using hand, mixer beat the softened butter and sugars until creamy. Add in the eggs and vanilla and mix just until combined.
Add the dry ingredients to the wet ingredients and mix until combined.
Scoop about 2 tablespoons of the dough and roll into balls and place on the baking sheet.
Bake for 11-12 minutes, let cool and remove to a cooling rack..
For the icing
In a small bowl whisk together the powdered sugar and milk until combined. If it's too thick add a little more milk until desired consistency.
Lightly dip the top of the cookies into the icing place them back on the cooling rack to dry.