Prepare the creamy vanilla pudding, but make these changes: double the recipe. In the doubled recipe, use 3-3/4 c milk, keeping all other ingredients and porportions the same. Cover with plastic wrap directly on the pudding and let cool to room temperature.
While the pudding is cooling, prepare the pastry and chill 30 minutes. Roll out pastry, fit into 10-inch pie plate, trim and flute. Bake as directed for a baked pie shell, and let cool.
When pastry and pudding are cooled to room temperature: slice bananas into coins. Layer into the pie shell: banana slices, then pudding, repeating until there are three layers of bananas and pudding in the pie shell. Chill in the refrigerator.
Before serving: whip the cream with vanilla and sugar. Top pie with whipped cream.