In a medium mixing bowl, combine the oats, flour, baking soda, salt, and cinnamon. Set aside.

In a large bowl, use an electric mixer to combine the butter, brown sugar, and granulated sugar until well combined.

Add the eggs and vanilla extract and beat on high until combined.

Spoon in the dry ingredients and mix on low speed until mixed, being careful not to overmix.

Cover, and chill the dough for 45 minutes.

Scoop about 1 ½ tablespoons of dough for each cookie, and place about 2-3 inches apart on the baking sheets.

Bake for 10-12 minutes until lightly browned on the edges.

Remove from the oven and let the cookies sit on the baking sheets for 8-10 minutes. Transfer to a wire rack to cool completely.

While the cookies cool, make the icing. Place the sifted powdered sugar in a shallow bowl. Add vanilla and 1 tablespoon of milk at a time, adding more until desired consistency is reached. The icing will be fairly thick.

Dip the tops of the cooled cookies by turning them upside down and dip in the icing. Pull the cookie straight up, letting the excess icing drip back into the bowl. Turn the cookie right-side-up and transfer back to the cooling rack. Allow the icing to set for 30 minutes before serving.