Preheat the oven to 350 degrees F. Line a large baking sheet with parchment paper.
Whisk the flour, baking powder, and salt in a medium bowl. In a separate bowl, beat the sugar, butter, lemon and orange zest with an electric mixer. Beat in the eggs one at a time. Stir in the pistachios and cranberries.
Form the dough into a 13-inch long, 3-inch wide log on the prepared baking sheet. Bake until light golden, about 30 minutes. Cool for 30 minutes.
Place the log on the cutting board. Using a sharp serrated knife, cut the log on a diagonal into 1/2-inch-thick slices. Arrange the biscotti, cut side down, on the baking sheet. Bake the biscotti until they are pale golden, about 12-15 minutes. Transfer the biscotti to a rack and cool completely.
The biscotti can be stored in an airtight container for up to a week (if they last that long!).