In the bowl of a stand mixer fitted with a paddle attachment or a large bowl, beat together the softened butter and sugar until light and fluffy.
Beat in the egg, followed by the vanilla extract.
In a medium bowl, combine the flour, dark cocoa powder, and salt. Beat into the butter mixture until just combined with no streaks remaining and a dough is formed.
Transfer the dough to a piece of plastic wrap and pat into a disc. Wrap in the plastic and refrigerate 1-2 hours until chilled.
Preheat oven to 350˚F (180˚C). Line two baking sheets with parchment or lightly grease.
Once chilled and no longer sticky when touched, remove the dough from the plastic wrap and place between two large pieces of parchment.
Roll the dough into a large sheet about 1/8-1/4 inch (3-6 millimeters) thick.
Gently remove the top parchment sheet and cut the dough into circles using a plain or fluted 2 1/2 inch (6 centimeter) round cutter.
Carefully transfer the rounds to the prepared baking sheets about 1 inch (2.5 centimeters) apart. If desired, stamp the top of the cookie with a design, taking care not to push all the way to the bottom.
Collect the scraps of cookie dough and roll out again between two sheets of parchment to make more cookies. If too soft to handle, refrigerate for about 30 minutes.
Bake the cookies in the preheated oven until set, about 8-10 minutes.
Allow to rest on cookie sheet for 5 minutes before transferring to a wire rack to cool to room temperature. Repeat with remaining dough.