Preheat oven to 375 degrees F. Line your baking sheet with parchment paper.
Add butter (or coconut oil) to the bowl of a stand mixer followed by the sugars. Using paddle attachment, mix slightly. Add in both eggs. Mix again until smooth. Note - If you're using coconut oil, measure it as solid, not melted.
Add in baking powder, soda, cinnamon, nutmeg, and vanilla. Mix.
Mix in oats. Then add in flour and mix again until just combined.
Scoop out dough and drop cookie dough balls about 2 inches apart on your prepared baking sheet. Flatten slightly. Bake for 8 - 10 minutes until edges are just golden brown. This allows for perfect texture of a light crisp to the outsides and a chewy center.
Cookies will come out looking a little puffy. Let them rest on cookie sheet for 3 minutes before transferring to wire rack. Cool cookies completely before frosting.
Once cookies have cooled completely, whisk together powdered sugar and milk in a shallow bowl until smooth. Dip tops of the cookies into icing. Set cookies aside in a single layer until the icing sets completely before storing them in an airtight container.