Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a medium bowl, whisk together the flour, cocoa powder, baking powder, and salt until well combined.
In a separate large mixing bowl, beat the sugar and eggs together until slightly thickened and pale, about 2 minutes. Add the vanilla extract and mix well.
Gradually add the dry ingredients to the egg mixture, stirring until just combined. The dough will be thick.
Fold in the chopped pistachios and chocolate chips until evenly distributed throughout the dough.
Transfer the dough to a lightly floured surface and shape it into a log about 12 inches long and 3 inches wide. Place it on the prepared baking sheet.
Bake for 25-30 minutes or until the log is firm to the touch. Remove from the oven and let it cool for 10 minutes.
Reduce the oven temperature to 325°F (160°C). After cooling, slice the log diagonally into 1/2-inch thick slices.
Arrange the biscotti slices cut side down back on the baking sheet. Bake for an additional 10-12 minutes. Flip the biscotti over and bake for another 10-12 minutes until they are firm and slightly dry.
Allow to cool completely on a wire rack, and if desired, dust with powdered sugar before serving.