Preheat oven to 350 degrees F and line cookie sheets with parchment paper. In a large bowl with an electric mixer or stand mixer, cream together the butter until smooth. Add the sugars and mix until light and fluffy. Be sure to scrape down the sides of the bowl with a rubber spatula.
Add in eggs one a time, molasses, then vanilla extract or paste. Continue to beat until combined.
In a medium bowl, whisk together the flour, oats, cinnamon, ginger, nutmeg, cloves, and baking soda together.
Add the flour mixture to the wet mixture and mix again until just dough has formed. Be sure not to over-mix. Scoop into 3 tablespoon dough balls (1 1/2 scoops of a mini ice cream scoop).
Break the dough balls in half then gently smoosh back together with the ridges facing up. This will help give the classic iced cookie look once dunked in the icing. Place on prepared baking sheet and bake for 8-10 minutes or until the edges are a light golden brown.
In the meantime, whisk together all of the icing ingredients until smooth. The icing should be thick.
Once the cookies are cooled, dunk each cookie in the icing and scraping any access off the side of the bowl. Place on a cooling rack and repeat. Let cookies sit until icing is set. Enjoy!