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Combine the flour, black cocoa powder, baking powder, salt, and baking soda in a medium bowl. Set aside.
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Place the chocolate in a microwave safe bowl and heat in the microwave at 50% power, stirring every 30 seconds, until melted.
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In a separate bowl, beat the butter until creamy, about 2 minutes. Add the granulated sugar and beat until light and fluffy, about 2 minutes.
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Add the egg and beat until combined. Add the vanilla extract and melted chocolate and beat on low speed until combined.
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Gradually add the flour mixture, beating until incorporated.
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Divide the dough in half, shape into a flat disk, and wrap in plastic wrap. Chill in the refrigerator until firm, about 4 hours.
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After firm, let the dough rest at room temperature for 30 minutes before rolling out.
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Preheat the oven to 350 F. Line baking sheets with parchment paper.
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Place 1 dough disk between two sheets of wax or parchment paper and roll out to ¼ to ½ inch thickness.
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Cut out cookies using the cat shaped cookie cutters. Transfer to the prepared baking sheets, placing them about 1 inch apart. Place the baking sheet with the cookies in the refrigerator for 10 minutes.
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Gather the dough scraps, re-roll, and cut out more cookies. Repeat until desired amount of cookies are cut out.
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Bake until cookies are firm on top and slightly darker around the edges, about 9-12 minutes. Cool cookies for 1-2 minutes on the baking sheet before transferring to a wire rack to cool completely.