Heat oven to 350ºF. Line baking sheet with parchment paper. In medium bowl, whisk together flour, cornmeal, ginger, baking powder, and salt.
In large bowl of stand mixer, beat sugar, oil, eggs, vanilla, and zest on medium until smooth and fully emulsified, about 2 minutes.
Reduce speed to low and gradually add flour mixture, beating until just fully incorporated (dough will be stiff). Mix in pistachios and cranberries.
On prepared baking sheet, with floured hands, shape dough into 3/4-inch-thick log about 12- by 4-inches. Flatten top. Bake, rotating pan halfway through, until light golden brown and top begins to crack, 32 to 38 minutes Let log cool 15 minutes.
Using serrated knife, slice log on slight diagonal 1/2 inch thick. Arrange slices, cut sides down, on same baking sheet in single layer. Bake, flipping biscotti halfway through, until golden brown, 6 to 8 minutes per side. Transfer to wire rack to cool.
Dip 1 end of each biscotto in melted dark chocolate, then drizzle white chocolate (with spoon or piping bag) on dark chocolate.