In a mixing bowl, combine chocolate cookie crumbs and granulated sugar. Pour in the melted unsalted butter and stir until the mixture resembles wet sand. Press this mixture firmly into the bottom of a 9-inch springform pan using the back of a measuring cup, creating an even layer. Chill the crust in the refrigerator for about 30 minutes to firm up.

In a large mixing bowl, beat well-softened cream cheese with an electric mixer until smooth and creamy, about 2 minutes. Gradually add in powdered sugar, vanilla extract, and peppermint extract, mixing until fully combined.

In a separate bowl, whip the heavy cream using an electric mixer on medium speed until stiff peaks form, about 3-4 minutes. Gently fold the whipped cream into the cream cheese mixture and incorporate crushed peppermint candies.

Pour half of the creamy filling over the chilled crust, spreading it evenly. Melt the semi-sweet chocolate chips in a microwave-safe bowl. Allow to cool slightly before spreading over the first layer of cheesecake. Top with the remaining filling.

Cover the cheesecake with plastic wrap and refrigerate for at least 4 hours, or ideally overnight, to allow the flavors to meld and the cheesecake to set.

Once set, carefully remove the cheesecake from the springform pan. Top with whipped cream, crushed peppermint candies, and optional chocolate shavings. Slice into wedges and serve chilled.