Preheat oven to 350 degrees. Line a baking sheet with parchment paper.
In a bowl, beat the cake mix, eggs, water, and oil together for 2 minutes. Spread into the prepared baking sheet and bake for 15 minutes or until a toothpick comes out clean.
Moisten a dish towel like a flour sack towel. Lay it out on the counter. Dust the top of the cake with cocoa powder and invert it onto the dish towel. Carefully remove the parchment paper and dust that side of the cake with cocoa powder. Carefully roll up the cake in the towel starting with the longest side of the cake. Allow to cool completely.
Once the cake is cooled, add the butter, cream, powdered sugar and peppermint extract for the filling. Beat together until well combined. Carefully unroll the cake and spread the filling over the cake and sprinkle with the 1/2 cup crushed candy canes. Roll the cake up carefully from the long side. Place the cake seam side down on a cooling rack with a baking sheet underneath it.
Place the dark chocolate chips and the 1/2 cup heavy cream in a microwave safe bowl. Microwave in 30 second interval stirring after each one until the chocolate chips are completely melted. Pour the ganache over the cake. Spread so the ganache coats the cake. You can always use the excess that falls through the cooling rack on to the baking sheet if needed.
Garnish with chocolate curls and extra crushed candy canes. Allow to set before moving to a serving platter. Serves 10.