Whip heavy cream in a cold bowl until stiff peaks form, then refrigerate.
Beat cream cheese in a large bowl until completely smooth.
Add sweetened condensed milk and mix until fully combined.
Mix in vanilla extract and peppermint extract.
Gently fold whipped cream into the cream cheese mixture until light and airy.
Spoon filling evenly into the chocolate crust and smooth the top.
Refrigerate for at least 4 hours, preferably overnight, until fully set.
Just before serving, sprinkle crushed candy canes on top.
Garnish with whipped cream and chocolate shavings or drizzle, if desired.