In a large mixing bowl, beat the heavy whipping cream until it becomes thick and forms stiff peaks. Set the whipped cream aside for later use.
In a separate medium bowl, blend the softened cream cheese with the powdered sugar until the mixture is smooth and creamy.
Add the vanilla extract, peppermint flavoring, and red food coloring to the cream cheese mixture. Continue mixing until the color is evenly distributed and the ingredients are fully incorporated.
Gently stir in ½ cup of crushed peppermint candy until the pieces are evenly dispersed throughout the filling.
Transfer the cream cheese mixture into the bowl with the whipped heavy cream. Mix on low speed until both mixtures are completely combined and the filling has a smooth, uniform texture.
Spoon the peppermint filling into the Oreo pie crust, then spread it evenly across the crust to create a level surface.
Cover the pie with a layer of thawed whipped topping, then scatter additional crushed peppermint candy over the top for garnish.
Refrigerate the pie for 1 to 2 hours, or until properly chilled and ready to serve.