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In a medium bowl, whisk together the flour, cocoa powder, baking powder, and salt. Set aside.
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In a large bowl, beat the butter until smooth and creamy. Add the sugar and beat until light and fluffy, about 2 minutes. Beat in the egg and vanilla, scraping the sides of the bowl as needed.
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Gradually add the flour mixture to the wet ingredients, beating on low until combined.
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Divide the dough in half, shape into two disks, and wrap in plastic wrap.
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Place dough in the refrigerator to chill for about 1 hour.
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After the dough has chilled, remove from the refrigerator and preheat the oven to 350 F. Line two baking sheets with parchment paper.
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Place one disk of dough between two sheets of parchment paper and roll out to about ½ inch thickness.
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Cut dough out using cutters, paper templates, or a mix of both. To make two train cars and one engine, you will need 9 rectangles, 6 squares, 5 front train pieces, 11 1-inch circles, and 2 ½ inch circles. Cut some extras too, in case one breaks.
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Place cut cookies onto prepared baking sheets and bake for 10 minutes. Cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.