Preheat the oven to 300°F. Line a baking tray with parchment paper or a silicone baking mat.
In a small bowl, mix together the ground flaxseed and 6 tablespoons (1/4 cup plus 2 tablespoons) warm water. Allow to sit for at least 5 minutes: this “flax egg” will help the biscotti hold together.
In a large bowl, mix together the olive oil and sugar. Add the vanilla extract, orange extract, and orange zest, and mix again. Finally, beat in the flax egg until well incorporated.
In a medium bowl, mix together the flour, salt, and baking powder, then add half the dry ingredients to the larger bowl of wet ingredients. Mix until combined, then add the remaining dry ingredients and mix again. Stir in the cranberries and pistachios, mixing well until there are no loose cranberries or pistachios in the bottom of the bowl.
Wet your hands to make working with the dough easier, and divide the dough in half. Place the dough on the prepared baking sheet, and use your fingertips to pat into rectangles roughly 8 inches by 4 inches, maintaining at least 2 inches of space between rectangles. Bake the dough for 30 to 35 minutes, until the dough is lightly browned and feels mostly firm to the touch. Remove from the oven, cover with a clean kitchen towel to keep the tops from drying out too much, and leave to cool for 15 minutes. Reduce the oven temperature to 275°F.
Transfer the logs to a cutting board, and use a serrated knife to cut into ¾-inch slices. Arrange cut-side up the baking tray, and bake for 10 to 12 minutes, until the biscotti are lightly browned and dry to the touch. (They don’t need to feel completely dried out, as they continue to crisp as they cool.) Remove from the oven, allow to cool for a few minutes, and then transfer to a cooling rack to cool completely.
