Whip the heavy cream until stiff peaks form.
In a large mixing bowl, beat the heavy whipping cream using either a hand mixer or a stand mixer. Continue whipping until the cream holds firm peaks when the beaters are lifted. Once you reach stiff peaks, set the whipped cream aside — you will fold other ingredients into it later.

Prepare the cream cheese mixture.
In a separate medium bowl, beat the softened cream cheese together with the powdered sugar until the mixture is smooth and free of lumps. Ensure the cream cheese is completely softened to room temperature before using. Next, add the vanilla extract, peppermint extract, and red food coloring. Blend until the color is even and the mixture is uniform. Finally, gently stir in ½ cup of crushed peppermint candy so you get bits of candy throughout.

Combine the whipped cream and cream cheese mixtures.
Carefully fold the cream cheese mixture into the whipped cream. Use a spatula or mixer on low speed. The goal is to combine thoroughly without deflating the whipped cream, resulting in a light, airy yet creamy filling.

Fill the Oreo crust.
Pour the combined filling into the prepared Oreo pie crust. Smooth the top evenly with a spatula so the filling sits level within the crust.

Top with whipped topping and garnish.
Spread a generous layer of thawed whipped topping over the pie filling. Then, sprinkle crushed peppermint candy on top for a festive, crunchy finish.

Chill before serving.
Place the pie in the refrigerator and chill for 1 to 2 hours, or until completely set and firm. Once chilled, slice and serve.