Step 1 In a medium bowl, sift together the flour, baking powder, cocoa powder and espresso powder, and set aside.
Step 2 In the bowl of a stand mixer fitted with the paddle attachment, or in a large bowl using a hand mixer, beat together canola oil, eggs and vanilla. Beat in the sugar, then gradually beat in the dry ingredients. Stir in 1 cup crushed candy cane pieces by hand.
Step 3Cover the mixing bowl and refrigerate the dough for at least 2 hours.
Step 4Heat the oven to 350 degrees. Line a large cookie sheet with parchment paper. Form the dough into 2 slightly flattened logs, each about 12 inches long and 3 inches wide. Place the logs a few inches apart on the prepared cookie sheet (the logs will spread as they bake) and bake for 25 minutes, rotating halfway through for even baking.
Step 5Remove and cool the logs for 20 to 25 minutes. Meanwhile, reduce the oven to 300 degrees. Cut the cooled logs crosswise into one-half-inch thick slices, and separate the slices about one-fourth inch, leaving the slices upright. Bake for an additional 10 minutes to set and begin to harden the cookies.
Step 6Cool completely, then drizzle with the melted white chocolate; you may not use all of the chocolate. Sprinkle over the remaining one-fourth to one-half cup crushed candy canes. Refrigerate the cookies to set the chocolate.