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1. Using a hand-held electric mixer, cream butter and cream cheese until fluffy, about 2 minutes. Add egg, 1 cup flour, sugar, baking powder, and vanilla. Beat on low speed until combined. Gradually add remaining cup flour. Using a wooden spoon, stir until fully combined. Divide dough in half. Shape each half into a disc, wrap in plastic, and refrigerate until firm, 1 to 2 hours.
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2. Preheat oven to 350 degrees. Line baking sheets with Silpat baking mats or parchment paper.
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3. Prepare the filling: Using a hand-held electric mixer, beat cream cheese and sugar until fluffy. With a wooden spoon, stir in coconut and chips. Set aside.
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4. Remove one disc of dough from refrigerator. Roll on a lightly floured surface into an 8-by-13-inch rectangle about 1/8-inch thick. With a fluted cookie cutter, cut into fifteen 2 1/2-inch squares. Place on prepared baking sheets, about 1 1/2 inches apart.
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5. Place 1 teaspoon filling in center of each square. Using a fluted pastry wheel, cut 1-inch slits diagonally from each corner toward the filling. Fold every other tip over to cover filling, and form a pinwheel. Press lightly to seal.
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6. Whisk together egg and oil. Using a pastry brush, lightly brush tops of pinwheels with egg mixture. Sprinkle with sugar.
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7. Transfer to oven, and bake until edges are golden and cookies are slightly puffed, 10 to 12 minutes. Transfer baking sheet to a wire rack to cool. Let cool for 5 minutes on baking sheets before transferring cookies to wire rack. Repeat with remaining disc of dough.
