Prepare and bake pie crust according to package directions for a baked shell; cool completely.
In medium mixing bowl, combine pudding mixes, 3 cups whipping cream, milk and 1 teaspoon vanilla. Beat 1 minute at medium speed with electric mixer. Allow pudding to stand until thickened (about 5 minutes).
Meanwhile, place 2/3 banana slices on bottom and sides of pie crust. Layer with ½ of pudding, remaining banana slices and remaining pudding; chill 1-2 hours.
In medium mixing bowl, combine remaining 1 cup whipping cream, remaining 1 teaspoon vanilla and sugar; beat on high speed with electric mixer until stiff peaks form. Spread whipped cream over top of pie. Sprinkle with toasted sliced almonds. Refrigerated up to 2 hours before serving.