For the dough: Mix together butter and sugar until well combined with either hand mixer or stand mixer, 2 to 3 minutes. Beat in the eggs and vanilla. Stir in flour, baking powder, and salt on low speed.
Using a 1 tablespoon cookie scoop, scoop dough onto cookie sheet and refrigerate for minimum 1 hour.
Preheat oven to 375 degrees F.
Bake for 9 to 11 minutes, until slightly golden. Sometimes, depending on how much you refrigerate them, they may take longer. Let cool on wax paper or cookie rack. Cookies will flatten slightly but should maintain most of their roundness.
For the frosting: Place the butter in stand mixer or medium bowl and beat on low speed until fluffy. Then slowly add the confectioners' sugar and milk, until it is well incorporated.
Add the vanilla and beat until fluffy, about 4 minutes. If frosting seems stiff, add more milk a small bit at a time until the desired consistency.
To assemble: Add 1 cup of coconut to a small bowl and set aside. Slowly add more when bowl gets low, 1 cup at a time.
Once cookies are cool, use a frosting spatula to spread the frosting over the tops. After frosting each individual cookie, dip them into the coconut bowl and evenly spread.
Place on platter or decorative plate to enjoy. For a more winter wonderland looking theme, sprinkle rock candy.
To make snowmen, stack 3 cookies on top of each other and decorate by adding a hat, buttons, nose, etc, get creative! Enjoy!