Preheat oven to 350 degrees. Line a large baking sheet with parchment paper.
In a medium bowl, whisk together flour, cocoa powder, baking powder, and salt until well combined; set aside. In the large bowl of an electric mixer, beat egg, egg yolk, and sugar until light and fluffy; beat in the vanilla and oil until well combined.
With the mixer on low, beat in dry ingredients until combined. Fold in walnuts, chocolate, and ginger with a rubber spatula (dough will be stiff).
With moistened hands shape the dough into 2 logs, each about 9 inches long and 2 1/2 inches wide. Bake until set on top, about 20 minutes. Cool 10 minutes in pan. Reduce oven temperature to 325 degrees.
Transfer logs to a cutting board and, with a serrated knife, cut each log on the diagonal into 16 slices, each 1/2 inch thick. Bake until crisp, about 20 minutes, turning the biscotti over midway through. Cool 5 minutes on a baking sheet, then transfer to a wire rack to cool completely. Store in an airtight container for up to a week.