Preheat oven to 350°F (175°C). Line a baking sheet with parchment paper or a silicone liner.
Combine the flour, baking powder, and salt. Set aside.
Using an electric mixer on medium speed, beat the butter, sugar, and brown sugar until light and fluffy. Add the eggs, one at a time, mixing well after each addition. Mix in the vanilla.
Reduce the mixer speed to low. Gradually add the flour mixture, mixing just until combined.
Divide the dough in half. Mix the cocoa powder into one portion of the dough.
Transfer the chocolate dough to the prepared pan. Shape the dough into a rectangle about 3 & 1/2" wide and 3/8" tall. The dough will be a bit sticky, so dust your fingertips with a bit of flour if necessary to help you shape it.
Place the vanilla dough on top of the chocolate dough. Shape to cover the chocolate dough. The finished rectangle should be about 3 & 1/2" wide and 3/4" tall.
Fold the dough by thirds, starting with a short end (like folding a letter). Shape the dough into a rectangle. about 3 & 1/2" wide and 3/4" tall. Repeat if you like.*
Bake for 25 minutes. Remove the pan from the oven and allow to cool for 10 minutes (or until the dough is cool enough to handle).
Use the parchment paper to transfer the biscotti to a cutting board. Cut the biscotti into 3/4" crosswise slices.
Line the baking sheet with a fresh sheet of parchment paper or clean silicone liner. Place the biscotti, cut side down, onto the pan.
Bake 18 to 22 minutes, or until browned. Cool on the pan for 10 minutes. Then transfer the cookies to a wire rack to cool completely.
Notes
*For more marbling, you can give the dough a twist in the places where you'll fold the dough. After twisting, roughly reshape if needed before folding.