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 speed and add vanilla and banana pudding mixes, whipping until pudding mixes are blended fully with the cream and the mixture thickens. Increase speed to high and beat until mixture is stiff.
Line the bottom and half way up the sides of pie crust with banana slices. Cover bananas with half of the banana cream mixture and top completely with banana slices. Top with the remaining banana cream mixture.
In a small bowl, whip 1 cup cream until stiff peaks form. Using a pastry bag, pipe cream onto top of pie, covering completely. Refrigerate 1 hour before serving.