In a small bowl, whisk together flour, baking powder, and salt.
In a standing mixer or large bowl, cream butter and sugar until light and fluffy, about 3 minutes. Add egg and vanilla extract. Reduce speed to low, then add flour mixture and mix until just combined – do not overmix.
Add cocoa powder, baking soda, and melted chocolate, and stir to combine (dough will be slightly stiff). On a sheet of waxed paper or plastic wrap, form the dough into a log (12 inches long, 2 inches in diameter); wrap and seal well. Chill at least 4 hours or freeze (defrost before slicing).
Heat oven to 375°.
Slice ¼-inch rounds from the log to fill an ungreased baking sheet. Dip your finger in water and moisten the edge of each cookie, then roll cookie in pistachios. Place in oven 6 minutes, turn baking sheet, and bake another 6 to 8 minutes.
Cool cookies 2 to 3 minutes on pan, then transfer to wire racks.