Preheat oven to 325°F.
In a medium bowl, whisk together the flour, cocoa powder, baking soda, baking powder and salt. Set aside.
In the bowl on an electric mixer, beat the butter until smooth, then add sugar, and continue to beat until fully incorporated. Add eggs, one at a time, while blending. Add vanilla.
While slowly blending, pour in bowl of dry ingredients, then chocolate chips. Blend just until combined.
Line a baking sheet with parchment paper or a silicone mat. Divide the dough in half. On a very lightly floured surface, roll the dough into two logs, almost the length of the baking sheet.
Transfer logs to the baking sheet, leaving space between the two. Gently flatten the logs down (with your hands) until the dough is about 1-1/4" to 1-1/2" tall. You should now have two rounded rectangles. They do not have to be perfect, but try to make sure the ends of the logs are almost as thick as the middle.
Bake logs for 30 minutes, until the dough feels firm to the touch. Remove from oven and allow to cool (on the baking sheet) for about 15 minutes.
Gently transfer the baked logs to a cutting board and use a sharp, serrated knife to cut the logs into thick slices (about 3/4 inch thick). Lay the cookies, cut side down, onto a baking sheets (you'll need two this time) and return to the oven. Bake one sheet at a time for 8-10 minutes, then carefully flip over each cookie, and bake an additional 8-10 minutes. Repeat with second sheet of cookies.
While the cookies cool, chop white chocolate into small pieces, then melt in a double boiler, or in a microwave at 50% power (in 30 second intervals). Dip cooled cookies into the white chocolate (scrape off excess as desired), then sprinkle crushed candy cane pieces on top. Move to a baking sheet or cooling rack and allow the white chocolate to fully set before packaging biscotti.