Preheat oven to 400°F (200°C). Line a baking sheet with parchment paper.
For cream puffs: In a medium saucepan, heat milk, butter, and ¼ cup (60 grams) water over medium heat until butter is melted. Add flour and sugar, and whisk until a thick paste begins to form. Use a flat spatula or wooden spoon to stir mixture until it begins to look like mashed potatoes. Continue to cook, stirring constantly, until a skin forms on the bottom of the pan, 3 to 5 minutes.
Transfer mixture to the bowl of a stand mixer fitted with the whisk attachment. With mixer on medium-low speed, beat until dough is warm to the touch, 1 to 2 minutes. Add eggs, one at a time, beating until combined after each addition for about 30 seconds. (Mixture may look broken but will come back together.) Beat in vanilla.
Transfer batter to large pastry bag fitted with a ½-inch round piping tip (Wilton 1A/Ateco #806). Pipe batter into 2-inch rounds about 2 inches apart onto prepared pan.
Bake for 15 minutes. Reduce oven temperature to 350°F (180°C), and bake until the tops of the puffs are golden brown, about 15 minutes.
Using a wooden pick, poke a hole in the center of each puff. Allow the puffs to cool completely.
For peppermint whipped cream: Add all ingredients to the bowl of a stand mixer fitted with the whisk attachment. Beat on medium speed until stiff peaks form, 2 to 4 minutes. Refrigerate until ready to use.
For ganache: Add cream to a medium microwave-safe bowl, and heat on high until steaming, about 1 minute. Add chocolate; let it stand for 1 minute and then whisk until the chocolate is completely melted and combined with the cream. (Heat mixture on low if chocolate does not fully melt.)
Finely chop the peppermint bark or break it into small pieces.
Transfer whipped cream to large pastry bag fitted with a ½-inch piping tip of your choice. Gently cut the tops off the cream puffs, and fill each with1 tablespoon (12 grams) ganache. Sprinkle with peppermint bark. Then pipe peppermint whipped cream on top. Place the top of the cream puffs on top.
Add a drizzle of chocolate ganache on top, and sprinkle with more chopped peppermint bark. Best served same day as assembled. Refrigerate in an airtight container for up to 2 days.
