Prepare filling: In a large glass bowl, whisk together pudding mix, milk, and extract until soft set, about 4 minutes. Fold in whipped topping and refrigerate until thickened.

Prepare ganache: In a microwave-safe bowl, heat chocolate chips and heavy cream, stopping to stir every 30 seconds until smooth. Stir in corn syrup and set aside to cool to room temperature.

Prepare cream puffs: In a medium saucepan, heat butter, sugar, salt and water over medium heat until the butter is melted. DO NOT BOIL.

Add all the flour and stir until it forms a stiff batter. Keep stirring until the mixture starts to look more like a dough. Keep stirring for several minutes until it becomes matte and leaves a film on the bottom of the pan.

Transfer dough to the bowl of a stand mixer. Mix on medium low for one minute. Add the whisked eggs gradually. Once they've all been added, change the mixer speed to medium high and beat just until dough is glossy.

Using a pastry bag with a 1 inch round tip (you could also just cut a wide opening), pipe puffs that are a couple inches tall and a few inches wide onto prepared baking sheet. Bake for about 15 minutes, until the pastries start to turn golden brown, then turn oven down to 325 and continue baking until they are entirely brown.

Remove and poke a small hole in each pastry to let steam escape. Let cool completely on the pans set on wire racks.

When ready to serve, assemble cream puffs: Cut the tops off the cream puffs and fill with white chocolate peppermint filling. Top with cream puff top, crushed peppermint candies, and chocolate ganache.