Preheat oven to 350, with racks set in upper and lower thirds. In a medium bowl, whisk together flour, baking powder and salt; set aside. Place 1/2 cup coconut into a small bowl; set aside. Place remaining coconut in a food processor; pulse until coarsely ground. Set aside.

Using an electric mixer, beat butter with sugars until light and fluffy. Beat in egg and vanilla. With mixer on low, gradually add flour mixture and ground coconut; mix just until combined.

Drop dough by level tablespoons onto two baking sheets, 1 to 2 inches apart. Bake until lightly golden around the edges, 10 to 12 minutes, rotating sheets halfway through. Transfer cookies to a wire rack to cool completely.

Dividing evenly, spread filling on flat side of half the cookies; sandwich with remaining cookies. Roll edges in reserved coconut, and chill until ready to serve.

Creamy Vanilla Filling

Using an electric mixer, beat 1/2 cup (1 stick) room-temperature unsalted butter until light and fluffy. With mixer on medium, beat in 1 cup confectioners’ sugar, 1/2 cup at a time, scraping down bowl as necessary. Add 1/2 teaspoon pure vanilla extract; increase speed to high, and beat until filling is light and fluffy, 5 minutes. Makes about 1 cup.