Preheat oven to 325 degrees. Prepare baking sheet by lining with a silicone baking mat. You can use parchment paper instead, but the mat holds in place much better when we form the biscotti log.
Place flour, cocoa powder, baking powder, and salt in a medium bowl and whisk together to combined. Set aside.
In a large bowl, whisk eggs, sugar, melted butter, oil, and extract just until combined. Add in half of the flour mixture and stir together with wooden spoon. Add remaining half of flour mixture and mix until just combined. Add nuts and fold into dough. Don't overmix.
Dump dough onto prepared baking sheet. Form dough into two even logs that are 8 inches long and 5 inches wide. Make sure to flatten out the top. Brush all sides with egg wash.
Bake for 25-28 minutes or until edges start to brown and toothpick comes out clean when inserted. Remove from oven but keep oven on. Let the logs cool for 15 minutes.
Using a serrated knife, slice biscotti into even 1-inch slices. Turn slices onto their sides so that the interior is facing up. Bake for 10-12 minutes and then flip and bake for another 10-12 minutes on the other side.
Remove from oven and let biscotti cool completely. They'll firm up as they cool. Serve at room temperature with your favorite hot beverage.