In a medium bowl, combine the crushed chocolate sandwich cookies and 1/4 cup of the chopped peppermint candies.
Pour the melted butter over the cookie mixture and stir until evenly coated.
Press the mixture firmly into the bottom and slightly up the sides of a 9-inch springform pan or pie dish. Chill in the refrigerator for at least 30 minutes.
In a separate bowl, use an electric mixer to beat the cold heavy cream until stiff peaks form, about 3 to 4 minutes. Place the whipped cream in the refrigerator.
In a large bowl, beat the softened cream cheese on medium speed until smooth.
Turn the mixer to low and slowly add the powdered sugar. Once incorporated, increase the speed to medium and beat until smooth.
Add the vanilla extract, peppermint extract, and food coloring, if using. Mix until the color is even.
Use a spatula to gently fold the chilled whipped cream into the cream cheese mixture until no streaks remain. Fold in 2/3 cup of the remaining chopped peppermint candies.
Spread the filling evenly over the chilled crust. Sprinkle the remaining chopped candies on top.
Cover tightly and chill in the refrigerator for at least 4 hours, or overnight, before slicing and serving.