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Preheat oven to 350 degrees with racks in upper and lower thirds. Whisk to combine flour, baking powder, and salt in a bowl. Reserve 1/2 cup coconut. Place remaining coconut in a food processor; pulse until coarsely ground.
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Beat butter and both sugars with an electric mixer on medium-high speed until fluffy, 3 to 4 minutes. Beat in egg and vanilla. Reduce speed to low, and gradually add flour mixture and ground coconut; mix until just combined.
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Drop dough by level tablespoons onto parchment-lined baking sheets, 1 to 2 inches apart. Bake, rotating sheets halfway through, until lightly golden around edges, 10 to 12 minutes. Transfer cookies to a wire rack to cool completely.
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Dividing evenly, spread filling on flat sides of half the cookies; sandwich with remaining cookies. Roll edges in 1/2 cup reserved coconut, and chill until ready to serve.