Preheat oven to 375 degrees F (190 degrees C). Grease 2 baking sheets.

Sift flour and baking powder together in a bowl. Beat white sugar and butter together in a separate bowl using an electric mixer until smooth and creamy; beat in eggs. Stir creamed butter mixture, cocoa powder, 2 tablespoons liqueur, and 2 teaspoons vanilla extract into flour mixture until dough is just combined.

Turn dough onto a lightly floured work surface and knead, adding flour as needed to keep from dough sticking to your hands. Roll dough, 1 to 2 tablespoons per cookie, in your hands and form a log-shape; twirl log into desired shape. Place cookies on the prepared baking sheet.

Bake in the preheated oven until edges of cookies are lightly browned, about 10 minutes.

Stir confectioners' sugar, 2 tablespoons liqueur, water, and 2 teaspoons vanilla extract together in a bowl until icing is creamy. Dip cookies into icing. Place a piece of waxed paper under a wire rack and place cookies on wire rack to cool.