Preheat the oven to 350°. Spread the pistachios in a pie plate and bake until golden, about 6 minutes; let cool. Turn the oven down to 325°.
In a small bowl, whisk the flour, baking powder, baking soda and salt. In a medium bowl, beat the butter with the sugar until light and fluffy. Beat in the eggs, 1 at a time, followed by the vanilla. At low speed, beat in the dry ingredients. With a wooden spoon, stir in the pistachios and cranberries.
Butter and flour a large cookie sheet. Pat the dough out on the sheet into two 14-inch-long logs 1 inch wide and 1 inch high; leave 3 inches between them. Bake in the lower third of the oven until golden, about 20 minutes. Transfer the cookie sheet to a rack; let the logs cool for 5 minutes. Using a serrated knife, slice logs on the diagonal 1/2 inch thick.
Bake the slices for 7 minutes on each side. Transfer the biscotti to a rack to cool completely. Drizzle with the melted white chocolate and refrigerate until set, about 10 minutes.
The biscotti can be kept in an airtight container for 1 week.