Preheat oven to 350 degrees. Line a 9" x 13" baking pan with aluminum foil. Spray foil with nonstick baking spray.
In the bowl of an electric mixure combine flour, sugar, and cocoa. Cut in butter. Mixture will be crumbly. Reserve 2 cups of the mixture and set aside. Press the remaining crumbs in the bottom of the prepared baking pan. Bake for 15 minutes.
While crust is baking in a large mixing bowl beat cream cheese until it's smooth. While mixer is going gradually add in sweetened condensed milk. Add egg and peppermint extract.
Pour cream cheese mixture over baked crust. Sprinkle white chocolate chips and crushed candy canes over cream cheese mixture.
Gently sprinkle the remaining chocolate mixture over the cream cheese layer. Gently press. Bake for 25 more minutes.
Cool until the bars are room temperature. Then chill. Cut into bars. Store leftovers in the refrigerator.