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Cream together the butter and sugar using a stand or a handheld mixer on medium.
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While still mixing on medium, add in the egg and vanilla extract.
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Turn the mixer on low and add in the flour ½ cups at a time.
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Add in the cocoa powder, salt, baking soda, and cornstarch.
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Cover the mixing bowl with plastic wrap and let chill in the refrigerator for 20 minutes.
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Preheat oven to 350 degrees and line a cookie sheet with parchment paper or a silicone baking mat.
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Spoon the cookie dough onto the paper or baking mat and bake for 9-10 minutes.
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Let cool on the cookie sheet for 2 minutes, then transfer to a cooling rack.
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While the cookies are cooling, prepare the cream filling by whipping the butter and shortening on medium speed with the whisk attachment for 1-2 minutes.
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Add in the powdered sugar ½ cup at a time, then the vanilla extract.
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Using a pastry knife or a butter knife, spread the cream filling on the bottom of one cookie, then place the other cookie on top.