In a large mixing bowl, add the vegan butter and cane sugar. Using a hand mixer or stand mixer, beat together until light, fluffy and fully combined.
Add the applesauce and vanilla. Continue to mix until fully combined. Set aside.
In a separate medium sized mixing bowl, sift the flour, cocoa powder, baking soda and baking powder. Stir in the salt.
Add the dry ingredients to the wet a little at a time, mixing after each addition. Until everything is fully combined. It may seem crumbly as you mix, but it will be perfect after everything comes together.
Cut two sheets of parchment paper to fit an 11x17 inch baking sheet. Then on a flat surface, put all of the cookie dough in the center of one piece of parchment paper.
Top the dough with the second piece of parchment paper and press to start flattening.
Using a rolling pin, roll the rolling pin over the top piece of parchment paper to roll all the dough out between the two pieces. You want to roll out evenly to match the size of the parchment paper. Then pick up the parchment and slide onto an 11x17 inch sheet pan. The cookie dough should fill the whole sheet pan now.
Leave the parchment on the bottom and top, and freeze for 20-30 minutes or until firm.
Preheat the oven to 350 degrees(F).
Peel the top layer of parchment paper off. Then bake for 20-25 minutes or until the top isn't shiny and it looks firm. The dough will most likely puff up, it will flatten as it cools.
Let the cookie base cool for a few minutes, then melt the white chocolate.
In a microwave safe bowl, melt the white chocolate in 30 second intervals. Stirring after each interval. Until the chocolate has melted, you should only need to do 2-3 intervals.
Add the peppermint extract to the white chocolate and whisk, add a little extra if you want it very pepperminty.
Pour the white chocolate over the cookie base and smooth out evenly. Sprinkle with crushed candy canes.
Let cool completely, then break into pieces. Keep in the fridge.