Preheat the oven to 350 degrees. Line a baking sheet with a silpat mat.
Combine the oats, flour, baking powder, cinnamon, baking soda, salt, nutmeg, and clove together in a bowl; mix well.
In a large bowl, beat the softened butter with the brown sugar and white sugar with a hand mixer until creamy.
Add the vanilla and egg; beat until combined.
Add the oat mixture to the butter mixture and stir until combined.
Scoop the dough into small balls spaced two inches apart.
Place into the oven and bake for 10 minutes, rotating the tray halfway through baking.
Remove from the oven and allow to cool for a few minutes before moving them to a wire rack to finish cooling completely.
While the cookies are cooling, make the icing by combining the powdered sugar with the vanilla and milk; mix well.
Once the cookies have cooled completely, drizzle the top with the frosting. Serve and enjoy.