Combine chocolate cookie crumbs, granulated sugar, and melted butter in a medium bowl. Press firmly into the bottom of a 9-inch springform pan and refrigerate for 15 minutes.

Beat softened cream cheese in a large bowl with an electric mixer until smooth. Gradually add powdered sugar, vanilla extract, and peppermint extract until fully combined.

Whip heavy cream in a separate bowl until stiff peaks form. Gently fold whipped cream into the cream cheese mixture, then incorporate crushed peppermint candies.

Pour half of the cheesecake filling over the chilled crust and smooth out. Melt semi-sweet chocolate chips in a microwave-safe bowl, stir until smooth, and pour over the filling.

Spread remaining cheesecake filling over the cooled chocolate layer, smoothing the top gently.

Cover the cheesecake with plastic wrap and refrigerate for at least 4 hours, preferably overnight.

Remove the side of the springform pan, top with whipped cream, additional crushed peppermint candies, and optional chocolate shavings before serving.