Using an electric mixer, whip 3 cups heavy cream on low speed until it starts to thicken. Add crushed ice and continue to whip another 4 minutes. Increase the speed and add vanilla and banana pudding mixes; whip until fully blended and the mixture thickens. Increase the speed to high and beat until mixture is stiff.
Line the bottom and halfway up the sides of the pie crust with banana slices. Cover bananas with 1/2 of the cream mixture, layer with remaining banana slices, and top with remaining cream mixture.
In a small bowl, whip remaining 1 cup cream until stiff peaks form. Using a pastry bag, pipe cream on top of pie until completely covered. Refrigerate for 1 hour before serving.