Preheat oven to 375°F. Line two baking sheets with parchment paper.

In the bowl of an electric mixer fitted with the paddle attachment, beat the butter until creamy. Gradually add the sugar and continue beating until light and fluffy. Scrape down the sides of the bowl with a rubber spatula. On low speed, add the vanilla, then the egg. Scrape down the bowl again. (Alternatively, a hand-held mixer can be used)

Meanwhile, add the flour, baking soda, and salt to a medium bowl. Add the cocoa powder and whisk until well incorporated.

With the mixer on low-to-medium, gradually add the flour mixture to the butter-sugar mixture, mixing well after each addition.

Roll out the dough to 1/8-inch thickness on a lightly floured board. (Or between two sheets of parchment or waxed paper.) Cut into it with a floured cookie cutter into shapes of about 2 1/2 inches in diameter. Place the cutouts on the prepared baking sheets with a small space between each.

Bake for 8 minutes. Allow the cookies to remain on the sheet for about one minute then carefully transfer them to a wire rack to cool.