1/2 cup (1 stick) chilled unsalted butter, cut into small pieces
1 large egg
1 teaspoon vanilla extract
1 1/2 cups all-purpose flour, (spooned and leveled)
Preheat oven to 350 degrees. Set aside 2 loosely packed cups of coconut on a plate. Place remaining coconut in a food processor along with sugar, salt, and baking powder; process until finely ground. Add butter, and process just until no lumps remain. Add egg and vanilla; process just until smooth. Add flour; pulse until a crumbly dough begins to form, scraping sides of bowl as needed (do not overmix).
Forming 5 or 6 at a time, scoop level tablespoons of dough, and place in reserved coconut. Roll into balls, coating with coconut.
Arrange balls, about 2 inches apart, on baking sheets. Bake until lightly golden, 23 to 25 minutes. Cool on baking sheets 1 to 2 minutes; transfer to a wire rack to cool completely.