Preheat the oven to 350 degrees and line a large baking sheet with parchment.
In a large mixing bowl add the flour, baking powder, salt, almonds, and pistachios. I used the bowl of my stand mixer. Whisk to mix well. Beat the 2 whole eggs and one egg yolk lightly in a small bowl.
Add the vanilla and orange zest. Make a well in the center of the dry ingredients and pour in the wet ingredients.
Using the dough hook on your stand mixer, mix the batter on low setting for a minute then increase to medium and continue to knead the dough for an additional three minutes.
You can also do this by hand but the dough is sticky and very stiff so the mixer is an easier alternative. If the batter is too dry add the extra egg white, a little at a time until a stiff but still sticky dough.
Divide the dough into half and spread each half out into a log shape about 6 inches long and 3 inches wide. Leave adequate space between the logs for them to expand when baking.
The dough is easier to handle if your hands are wet otherwise it will just stick to your hands. Gently flatten each log to about an inch thick because it will rise during baking.
If you have any of the egg white left you can brush the tops of the logs with it to aid browning. If you used it, no need to crack another egg, just leave it off.
Bake the biscotti for 17 to 20 minutes or until they are lightly golden brown and the top center feels firm to the touch. Reduce the oven temperature to 300 degrees.
Allow the logs to cool slightly then cut into ¾ inch slices. Place the slices with the cut side down back on the parchment paper. Return the biscotti to the oven and bake an addition 8-10 minutes until they are crispy.
Remove from the oven and allow to cool completely. Pour the chocolate chips into a microwave safe sallow dish and heat for one minute. Remove from the microwave and stir.
Continue melting the chocolate at 15 second intervals, stirring in between. When the chocolate is completely melted and smooth dip the bottoms of the biscotti in the chocolate and place on a cooling rack, chocolate side facing up.
Sprinkle the cookies with the chopped pistachios and allow the chocolate to harden before eating.