Preheat oven to 350 degrees. Put butter and sugar in a large bowl; beat until smooth. Add egg yolk, flour, cocoa, vanilla, baking powder, and salt; mix until well blended and smooth.
Divide dough in half. Roll out one piece between two sheets of parchment paper 1/4 inch thick. Repeat with remaining piece. Stack dough (still between parchment paper) on a baking sheet; freeze 15 minutes.
Working with one piece at a time, cut out dough with a 3-inch-high Z-shape cookie cutter, easing out shapes onto parchment-lined baking sheets as you work. Refrigerate shapes until firm, about 15 minutes.
Bake, rotating sheets halfway through, until firm, about 12 minutes. Let cool completely on sheets on a wire rack.