In a mixing bowl, combine the crushed graham crackers with the melted butter. Mix until well combined, resembling wet sand.
Press the graham cracker mixture firmly into the bottom and up the sides of a 9-inch pie dish to form the crust. Place in the refrigerator to chill for 15 minutes.
In another bowl, beat the softened cream cheese until smooth. Add the powdered sugar and vanilla extract, and mix until fully combined.
In a separate bowl, whip the heavy cream until stiff peaks form. Gently fold the whipped cream into the cream cheese mixture until fully incorporated.
Stir in the crushed candy canes and peppermint extract until evenly distributed.
Pour the filling into the chilled graham cracker crust, smoothing the top with a spatula.
Cover the pie with plastic wrap and refrigerate for at least 4 hours or until set, preferably overnight to enhance the flavors.
Before serving, drizzle chocolate syrup over the top and sprinkle with additional crushed candy canes for garnish.