Cream the butter and sugar together with a whisk. Whisk in the eggs (one at a time), vanilla, and spices. Add the baking soda, baking powder and flour. Mix until just incorporated – the dough will be wet and sticky.
Scoop cookie dough and using wet hands form into a ball about the size of a golf ball. Place onto a parchment lined baking sheet (don’t press down on the balls, you want the cookies to have that pillowy dome shape).
Bake at 350*F for 10 minutes or until light golden brown. The cookies should still be very soft and look underbaked. Let them cool on a rack before frosting.
While the cookies are cooling combine the icing sugar in a small bowl with the coconut. Slowly add coconut milk 1 tsp at a time, making sure that the first tsp is fully incorporated before adding the next. The frosting should be thick and spreadable with a butter knife. If not, add more coconut milk (sparingly!) or icing sugar until the desired consistency is reached.
Spread the frosting on the cooled cookie and allow it to harden before eating.