In a mixing bowl, combine the graham cracker crumbs and melted butter. Mix until the crumbs are well coated and resemble wet sand.

Press the graham cracker mixture evenly into the bottom of the 9-inch springform pan to form the crust. Make sure it is tightly packed down.

In another mixing bowl, combine the softened cream cheese and powdered sugar. Use an electric mixer or whisk to blend until smooth and creamy.

Add the vanilla extract and peppermint extract to the cream cheese mixture, mixing until well combined.

In a separate bowl, whip the heavy cream until stiff peaks form.

Gently fold the whipped cream into the cream cheese mixture using a rubber scraper. Be careful not to deflate the whipped cream.

Pour the cheesecake filling over the prepared crust in the springform pan, spreading it evenly with a spatula.

Cover the cheesecake with plastic wrap or aluminum foil and refrigerate for at least 4 hours, or until set.

Before serving, garnish the top with crushed peppermint candy for added flavor and decoration.