In a mixing bowl, combine the graham cracker crumbs and melted butter. If desired, add the cocoa powder for a chocolate flavor. Stir until well combined, then press the mixture evenly into the bottom of a 9-inch springform pan.
Refrigerate the crust while preparing the filling.
In another mixing bowl, combine the softened cream cheese, powdered sugar, vanilla extract, and peppermint extract. Using an electric mixer, beat the mixture until smooth and creamy.
In a separate bowl, whip the heavy cream until stiff peaks form. Carefully fold the whipped cream into the cream cheese mixture until fully incorporated.
Gently fold in the crushed peppermint candies, ensuring even distribution throughout the filling.
Pour the filling over the chilled crust, spreading it evenly. Smooth the top with a rubber spatula.
Cover the springform pan with plastic wrap and refrigerate for at least 4 hours or until set.
Once set, carefully remove the sides of the springform pan. Garnish the top with additional crushed peppermint candies before serving.