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1
In a large bowl, with an electric mixer on medium speed, beat butter and sugar until smooth. Add egg yolks, whole egg, rum, and vanilla and beat until well blended.
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2
In another bowl, mix 2 cups flour, cornstarch, and baking powder. Stir or beat into butter mixture until well blended. Divide dough in half. Flatten each portion into a disk, wrap in plastic wrap, and freeze until firm, about 30 minutes.
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3
Unwrap dough. On a lightly floured surface, with a floured rolling pin, roll one disk at a time to about 1/8 inch thick. With a floured 2- to 3-inch round cutter, cut out cookies. Place about 1 inch apart on buttered or cooking parchment-lined 12- by 15-inch baking sheets. Gather excess dough into a ball, reroll, and cut out remaining cookies.
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4
Bake in a 350u00b0 oven until cookie edges are golden, about 10 minutes; if baking more than one pan at a time, switch pan positions halfway through baking. Let the cookies cool on sheets for 5 minutes, then use a wide spatula to transfer them to racks to cool completely.
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5
Turn half the cookies bottom side up and spread each with about 1 tablespoon dulce de leche. Top with remaining cookies, bottom side down. Place coconut in a shallow bowl. Gently squeeze each sandwich until filling begins to show at the edges, then roll edges in coconut.
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6
Nutritional analysis is per sandwich cookie.
