In a medium bowl, cream the butter and sugar with a flexible spatula until smooth, about 1 minute.
Add the egg and vanilla and stir until well combined.
Place a fine-mesh sieve over the bowl and sift in the flour. Fold with the spatula until the flour is fully incorporated and the dough comes together.
Shape the dough into a disc, then cover with plastic wrap, and refrigerate until firm, at least 30 minutes to overnight.
Meanwhile Using thick paper and a craft knife, cut out a round stencil of your choosing. Set aside.
Cut a square from a double layer of cheesecloth. Place the cocoa powder in the center. Gather the edges, twist, and tie with kitchen string to create a sachet.
Preheat the oven to 350˚F (180˚C). Line a baking sheet with parchment paper.
Lightly dust a clean surface with flour. Place chilled dough on work surface and lightly dust with flour. Roll the dough out to ¼-inch (6-mm) thick, lifting and turning the dough as you roll to keep it from sticking. Using a 2-inch (5-cm) round cookie cutter, cut out rounds of dough. Gather scraps of dough and reroll to cut out more rounds, lightly dusting the work surface with flour as needed.
Place the rounds on the prepared baking sheet, spacing 1 inch (2 ½ cm) apart.
Place the stencil over a dough round, making sure to press down, and gently dab with the cocoa powder sachet to cover completely.
Bake the cookies for 10 minutes, rotating baking sheet halfway through, until pale golden. Let cool for 5 minutes on the baking sheet, then transfer to a wire rack to cool completely.