Preheat oven to 350ºF degrees. Line a large baking sheet with parchment paper or a silicone baking mat. Lightly flour the baking sheet. Set aside.

In a medium size bowl, whisk together butter, oil, egg, vanilla, and sugar until combined. Set aside.

In a large bowl, toss together the flour, baking powder, salt, pistachios, and white chocolate chips. Add the wet ingredients to the dry ingredients and gently mix with a large wooden spoon or sturdy rubber spatula until everything is combined.

Turn dough out onto lightly floured baking sheet and, with floured hands, pat dough into a rectangle about ½" thick. My rectangle was 6" wide and 7 and ½" long (using a ruler or a ruled silicone baking mat is helpful here). Brush entire slab (top and sides) with egg wash.

Bake dough slab for 20-22 minutes, or until the top and sides of the slab are lightly browned. Remove from the oven, but do not turn off the heat. Place baking sheet on a wire rack and allow to cool for 10 minutes. Once the dough is cool enough to touch, cut into 1" thick slices using a sharp knife. Cut these 1" slices in half, making a perpendicular slice down the entire slab. Set slices cut sides up on the baking sheet. Return to the oven to bake for 9 minutes. Remove from oven, turn biscotti over, and bake the other side for 9 minutes. Remove from the oven and allow to cool for 3 minutes on the baking sheet (cookies will become crunchy as they cool). Transfer biscotti to a wire rack to cool completely before serving. Biscotti stay fresh in an airtight container up to 2 weeks. Baked biscotti may be frozen up to 3 months.