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In a stand mixer bowl, cream together the butter and sugars together. Add in the egg and vanilla extract and mix on medium speed.
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Slowly add in the flour at ½ cup at a time until thoroughly mixed together.
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Add in the cocoa powder, salt, and baking powder. After everything is mixed together, then add in the red food coloring.
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Cover with plastic wrap and place in the refrigerator at least an hour.
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Preheat oven to 350 degrees and line a cookie sheet with parchment paper or a silicon baking mat.
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Using a spoon, spoon out the red velvet cookie dough and roll into a medium ball, then flatten down with your hands.
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Bake for 9-10 minutes. Allow the cookies to cool completely.
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Prepare the frosting by cream together the cream cheese and butter. Add in the powdered sugar ½ cup at a time and mix on low.
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While still mixing on low add in the vanilla extract.
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Using a pastry knife or a butter knife, spread the cream cheese frosting on the bottom of one cookie, then place another cookie on top. Repeat until there are no more cookies left.