In a medium bowl, whisk together flour, baking powder, and salt; set aside.
In the bowl of a stand mixer fitted with a paddle attachment, cream butter and sugar until well blended, 1 to 2 minutes. Add egg and vanilla extract, beat until well combined.
With the mixer on low, gradually add the flour mixture, scraping down sides of bowl, until combined. Remove half of the dough; set aside.
Add espresso powder, melted chocolate and cocoa powder to the remaining dough, beat until well combined.
Remove the chocolate dough from the mixer and shape into a squared off block, about 2-inches tall and wide, and 6 inches long. Do the same with the vanilla dough. Wrap both chocolate and vanilla dough in plastic wrap, separately, place on a baking sheet and refrigerate for 1 hour.
Cut each block into equal thirds lengthwise, then into thirds lengthwise again for checkering (a ruler comes in handy for this step).
Place 3 strips of dough on a piece of plastic wrap, alternating white and chocolate strips. Gently press strips together. Repeat steps forming second and third layers, alternating colors to create a checkerboard effect. Wrap assembled log in plastic. Repeat process for second log, reversing color pattern. Refrigerate 30 minutes, or freeze 15 minutes.
Preheat oven to 350 degrees. Line a baking sheet with parchment paper or a Silpat baking mat.
Slice each log into 1/4-inch-thick slices; place on baking sheet. Bake 10 to 12 minutes. Remove baking sheet from oven, and let cookies cool 2 minutes. Transfer cookies to a wire rack to cool completely.