Preheat oven to 375 degrees F (190 degrees C). Line cupcake tins with paper cupcake liners.
In a large bowl, stir together the flour, 3/4 cup cocoa powder, sugars, baking soda, baking powder and salt.
Make a well in the center and pour in the eggs, coffee, buttermilk and oil. Stir like crazy until smooth.. Spoon the batter into the prepared cups, dividing evenly. Bake in the preheated oven until the tops spring back when lightly pressed, about 25 minutes. Cool in the pan set over a wire rack.
While the cupcakes bake, prepare the ganache. Place white chocolate in medium heat proof bowl. Heat heavy cream in small pot until ALMOST to a boil, immediately pour over the chocolate. Allow to sit for 5 minutes then stir until smooth. Allow to cool. When it has cooled, add the crushed candy canes and fold in. (If you want it to be crunchy, use within the day. If you want it to have some liquid pockets, allow it to age a day or two in the fridge. You can bring it back to room temperature before using again.)
To get the ganache into the center, cut a cone shape out of the top of the cupcake. Fill the cup you have just made and place the cone of the cake back on top. (For extra filling, tear some of the cake off of the cone to fit more filling in.)
In mixer set on medium speed, beat the butter until smooth and silky. Turn the speed to low and add the pudding mix, when it is all incorporated, slowly add the cream, a little at a time. When fully incorporated bring speed up to high and beat for 5-7 minutes. Turn speed back down to low and add peppermint extract and powdered sugar by Tbsp., tasting along the way. When it is sweet to your taste, beat again at high speed for a good 5 minutes to really break down any graininess that you might get from the powdered sugar. Bring back down to low speed and beat for a while that way to get rid of air bubbles.
When the cupcakes have cooled, frost them with the buttercream.
Note: To get the “swirl” effect seen in some of the photos, paint three stripes of red gel food coloring inside your piping bag, then fill the piping bag with the buttercream.