Divide the basic sugar cookie dough in half (do not substitute slice-and-bake dough in this recipe).
On a floured surface, roll each piece out ¼ inch thick. Cut into rounds with a 1¾-inch cookie cutter. Place on baking sheets.
Top with a mixture of 1 egg white, 2 cups sweetened shredded coconut, and ¼ cup confectioners’ sugar.
Bake at 350° F on parchment-lined baking sheets until just beginning to brown, 12 to 15 minutes.
Cool slightly on baking sheets, then transfer to wire racks to cool completely.