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Beat butter, cream cheese, and sugar in the bowl of an electric stand mixer fitted with a flat beater until fluffy, about 3 minutes.
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Add egg and vanilla and beat to combine.
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Whisk together flour and baking powder, and salt.
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Put mixer on low speed and add flour. Beat until just combined (do not over-mix).
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Divide the dough in half and shape into disks. Wrap disks in plastic wrap and refrigerate for at least 2 hours or overnight.
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Preheat oven to 375 degrees F.
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Sprinkle work surface lightly with flour.
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Remove 1 wrapped pack of dough from refrigerator and let it soften slightly (about 10 minutes).
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Sprinkle rolling pin with flour and roll out dough to 1/8-inch thick. Move the dough around frequently to make sure it is not sticking. Use shaped cookie cutters to cut cookies.
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Place cookies at least 1-inch apart on a baking sheet lined with parchment or non-stick baking mat. Bake 7 to 9 minutes, until cookies are just beginning to turn light brown around the edges.
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Cool cookies on baking sheet for 1 minute then transfer to a wire rack. Cool completely.
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Repeat steps with remaining dough. You can gather up excess dough after cutting the cookies, shape into another disk, and roll out for more cookies. The texture may vary with re-rolled dough.