Preheat your oven to 400°F (200°C). This ensures that the cream puffs will rise perfectly. As the oven heats up, line a baking sheet with parchment paper to prevent sticking.
Prepare the cream puff dough: In a medium saucepan, combine whole milk, salted butter, and water over medium heat. Stir occasionally until the butter is melted. You’ll want the mixture to be warm but not boiling.
Add dry ingredients: Once the butter has melted, add all-purpose flour and granulated sugar to the saucepan. Whisk the mixture until it forms a thick paste, which should resemble mashed potatoes. Continue to cook, stirring constantly, for about 3 to 5 minutes until a skin forms on the bottom of the pan.
Mix with a stand mixer: Transfer the dough to the bowl of a stand mixer fitted with a whisk attachment. Mix on medium-low speed until the dough is warm to the touch, which should take about 1 to 2 minutes.
Add eggs: Incorporate large eggs one at a time, beating well after each addition. The dough may look broken at first, but keep mixing until it comes back together smoothly. This is a crucial step for that perfect puff.
Pipe the batter: Transfer the dough into a large pastry bag fitted with a ½-inch round piping tip. Pipe the batter into 2-inch rounds on your prepared baking sheet, leaving about 2 inches of space between each.
Bake the cream puffs: Place the tray in the oven and bake for 15 minutes. After this, reduce the temperature to 350°F (180°C) and continue baking until the tops are golden brown, which should take another 15 minutes. The key is to keep the oven door closed during this time to allow them to puff properly.
Poke holes in puffs: Once baked, take them out of the oven and use a wooden pick to poke a hole in the center of each puff. This step allows steam to escape, preventing them from becoming soggy.
Cool the puffs completely: Let the cream puffs cool completely on a wire rack, which will help them maintain their crispiness.
Make the peppermint whipped cream: In a clean bowl, add 2½ cups of cold heavy whipping cream, confectioners’ sugar, and peppermint extract. Beat on medium speed until stiff peaks form, which usually takes about 2 to 4 minutes. Refrigerate until ready to use.
Prepare the ganache: In a medium microwave-safe bowl, heat the remaining heavy whipping cream until steaming, about 1 minute. Add the dark chocolate and let it sit for 1 minute before whisking until smooth. If needed, heat on low until fully melted.
Chop the peppermint bark: Finely chop or break the peppermint bark into small pieces for sprinkling.
Fill the cream puffs: Transfer the peppermint whipped cream to a pastry bag. Gently cut the tops off each cream puff, fill them with about 1 tablespoon of ganache, and sprinkle with chopped peppermint bark. Pipe the whipped cream on top and replace the tops of the puffs.
Finish with ganache: Drizzle the remaining ganache on top and sprinkle more peppermint bark. These puffs are best served the same day they are assembled, but they can be stored in an airtight container for up to 2 days.