In a medium bowl, whisk together flour, baking powder, and salt. Set aside.
Reserve ½ cup coconut and set aside. Place remaining coconut in a food processor and pulse until coarsely ground.
In a standing electric mixer, beat butter and both sugars on medium-high speed until mixture is fluffy, about 3-4 minutes. Beat in egg and vanilla. Reduce speed to low and add flour mixture and ground coconut gradually, just until combined. Do not over mix.
Using a small cookie scoop (I use OXO), scoop a level scoop and place on a Silpat or parchment lined cookie sheet 1-2 inches apart. Bake until lightly golden around edges about 10-12 minutes
Meanwhile, make the filling. In a standing electric mixer, beat butter on medium-high speed until creamy, about 2 minutes. Reduce speed to medium and gradually beat in confectioners' sugar. Beat mixture until pale and fluffy, about 5 minutes. Add vanilla and beat until well combined.
Dividing evenly (eyeball it), spread filling on flat side of half the cookies. Top with second half of cookies. Roll edges in reserved coconut and chill until set or overnight for a softer cookie (Yay). Store cookies in the fridge.