Prepare the Crust

1. Preheat Oven: Preheat your oven to 325°F (160°C). Grease a 9-inch springform pan or line the bottom with parchment paper.
2. Mix Ingredients: In a medium bowl, combine chocolate cookie crumbs, melted butter, and sugar. Stir until the mixture resembles wet sand.
3. Press Into Pan: Press the mixture evenly into the bottom of the prepared pan to form the crust. Use the back of a spoon or the bottom of a glass to smooth it out.
4. Bake: Bake for 10 minutes, then set aside to cool while preparing the filling.

Make the Filling

1. Beat Cream Cheese: In a large mixing bowl, beat the softened cream cheese with a mixer on medium speed until smooth and creamy.
2. Add Sugar and Extracts: Gradually add sugar, vanilla extract, and peppermint extract, mixing until fully incorporated.
3. Add Eggs: Beat in the eggs one at a time, ensuring each is fully blended before adding the next.
4. Mix in White Chocolate: Slowly mix in the melted white chocolate until smooth and uniform.
5. Pour Filling: Pour the filling over the prepared crust, smoothing the top with a spatula.

Bake the Cheesecake

1. Prepare a Water Bath: Wrap the bottom of the springform pan in foil to prevent leaks. Place the pan in a large roasting dish and pour hot water into the dish until it reaches halfway up the sides of the pan.
2. Bake: Bake the cheesecake for 55-65 minutes, or until the edges are set but the center jiggles slightly when shaken.
3. Cool Gradually: Turn off the oven and crack the door open slightly. Let the cheesecake cool in the oven for 1 hour to prevent cracking.
4. Chill: Transfer the cheesecake to the refrigerator and chill for at least 5 hours or overnight.

Add the Topping

1. Whip Cream: In a cold mixing bowl, whip heavy cream with powdered sugar and peppermint extract until soft peaks form.
2. Spread or Pipe: Spread or pipe the whipped cream over the chilled cheesecake.
3. Decorate: Sprinkle crushed peppermint candies and white chocolate shavings over the top for a festive touch.