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Cream the butter, oil, sugar, vanilla, and salt in the bowl of a stand mixer fitted with a paddle attachment, just until the mixture is smooth.
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Add the egg and mix just until incorporated. Mix in the flour and cocoa powder keep mixing until fully incorporated. The dough will be crumbly.
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Transfer the dough to a parchment paper and form it into a ball. Roll the dough ball to a thickness of 3/8-inch, between two sheets of parchment paper. Cut shapes using a cookie cutter.
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Place the cookies on a baking sheet lined with parchment paper, and chill in the freezer for 15 min.
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Heat the oven to 375°F/190°C. Bake the cookies for 7-10 mins, or until the cookies look dry on the surface, and feel firm around the edges and set in the middle.
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Let the cookies cool completely before eating or storing them.