Preheat oven to 350ºF.
Line a large baking sheet with parchment paper; set aside.
Place chopped pistachios onto a baking sheet and transfer to the preheated oven. Toast them for 6 minutes, flipping halfway through cooking. Remove from the heat and transfer to a bowl to cool off; set aside.
Meanwhile, in a small skillet over medium heat, toast almonds until golden brown, about 5 minutes, flipping them often. Remove from the heat and transfer toasted almonds in a bowl to cool off; set aside.
In a medium bowl, combine flour, baking powder and salt; whisk until the ingredients are well mixed; set aside.
In the bowl of a stand mixer, combine eggs, sugar, oil and orange zest; process for 1 ½ minutes on medium speed.
Add the flour mixture and process on low speed until the dough is soft, about 4 minutes, stopping a few times to scrape the sides of the bowl.
Add toasted pistachios and toasted almonds, dried cranberries, orange juice and vanilla extract; process until well blended, about 1 to 1 ½ minutes, stopping to scrape the sides of the bowl.
Transfer the dough (it will be very sticky) to a lightly floured work surface. Sprinkle on flour and roll (not kneading) the dough in the flour until it's less sticky and easier to handle.
Divide the dough into 2 pieces and shape them into logs, about 10-inches long by 3-inches wide.
Place the logs on the prepared baking sheet and transfer to the preheated oven; bake for 40 to 45 minutes or until golden.
Remove from the heat and transfer to a cutting board to cut them into ½-inch thick slices with a serrated knife.
Transfer the biscotti to a wire rack placed on a baking sheet to cool off for 30-45 minutes.
Return the sliced biscotti to the baking sheet and bake for 10 minutes. Flip them over and bake for an additional 10 minutes.
Remove from the heat and let them cool off completely before serving and storing. Makes 24-28 biscotti.