To prepare the cookie dough: Preheat oven to 180°C/350°F. Grease/Spray a large baking sheet with non-stick cooking spray. Set aside.
In the electric mixer with a paddle attachment, cream butter and sugar until fluffy. Add one egg at a time, beating well after each addition, until just incorporated into the dough. Add both the flour and the cocoa powder, beating only until mixture is homogeneous. Stir in the vanilla.
Scoop dough with a cookie scoop and drop over the greased baking sheet, spacing at 2 inch (5 cm) intervals. Bake for 8 to 10 minutes. Transfer baking sheet to a rack and let cookies rest for about 3 to 5 minutes or until they can be handled without breaking apart.
Meanwhile, prepare the topping. In a small bowl, whisk in the sugar and coconut milk together until smooth. Spread the icing on top of each of the slightly warm cookies in a circular motion, sparing the edges. Let rest for 3 to 5 minutes. Dip each cookie, icing-side down, into shredded coconut, or simply place a mound of shredded coconut on top of the cookies. Drip a bit of icing on the center of the cookies to serve as glue for the mini eggs, and decorate with 3 mini eggs. Enjoy!