Preheat oven to 350ºF. Place chopped pistachios onto a baking sheet and transfer to the preheated oven. Toast them for 6 minutes, flipping half way 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 quite often. Place toasted almonds in a bowl to cool off; set aside.
In a medium bowl, combine flour, baking powder and salt; whisk until ingredients are well mixed; set aside.
In a bowl of a stand mixer, combine eggs, sugar, oil and orange zest; process for 1 ½ minutes on medium speed. Add flour mixture and process on low speed until the dough is soft, stopping a few times to scrape the sides of the bowl, about 4 minutes.
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 (very sticky) on a lightly work surface and sprinkle with flour. Roll (not kneading) the dough in flour until less sticky and able to handle it. Divide dough into 2 pieces and shape into logs around 10-inch long by 3-inch wide. Place logs on a large baking sheet lined with parchment paper and transfer to the preheated oven; bake for 40 to 45 minutes or until golden.
Remove from heat and transfer to a cutting board to slice into ½-inch thick with a serrated knife. Transfer the biscotti on a wire rack placed on a baking sheet to cool off for 30-45 minutes.
Return the sliced biscotti 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.