Add 1 1/2 cups of the whipping cream and powdered sugar to a large mixing bowl and beat with an electric mixer until stiff peaks form. Set aside.
In a separate bowl, beat the cream cheese with an electric mixer until smooth, about 1 minute. Add the sugar and peppermint extract and beat until combined.
Add the white chocolate and remaining 4 tablespoons of the heavy whipping cream in a microwave-safe bowl. Microwave at 50% power in 30 second increments, stirring between each one, until melted. Cool slightly for a few minutes.
Add the melted white chocolate to the cream cheese mixture and beat until completely combined.
Fold in the whipped cream to the cream cheese mixture, gently, until completely combined.
Fold in Andes peppermint bark baking chips to the mixture and pour the filling into the crust.
Refrigerate for at least 4 hours, preferrably overnight.