Prepare and bake the crust.
To make the filling, combine 2 cups milk, sugar and salt in a non-reactive saucepan; whisk once to mix and bring to a boil over low heat. Place remaining 1/2 cup milk in a mixing bowl and whisk in cornstarch, then eggs. Return milk and sugar mixture to a boil over low heat then whisk about a third of it into the egg mixture. Return milk and sugar mixture to a boil once more and whisk in the egg mixture, whisking constantly until the filling thickens and comes to a boil. Allow to boil, whisking constantly, for about 30 seconds. Remove from heat, whisk in butter and vanilla; pour into a non-reactive bowl. Press plastic wrap against the surface of the filling and chill until it is approximately 75 degrees. Fold the bananas into the cooled filling and spread it evenly in the cooled crust.
To finish the pie, whip the cream with the sugar and vanilla until it holds a firm peak. Use a hand mixer on medium speed or a heavy-duty mixer fitted with the whisk. Spread the cream over the filling, making sure it touches the edges of the crust all around.
To mix the dough by hand, combine flour, salt and baking powder in a medium-sized mixing bowl and stir well to mix. Cut butter into 1-tablespoon pieces and add to dry ingredients. Toss once or twice to coat pieces of butter. Then using your hands or a pastry blender, break the butter into tiny pieces and pinch and squeeze it into the dry ingredients. Keep the mixture uniform by occasionally reaching down to the bottom of the bowl and mixing all the ingredients evenly together. Continue rubbing the butter into the dry ingredients until the mixture resembles a coarse-ground cornmeal and no large pieces of butter remain visible. Sprinkle the minimum amount of water over the butter and flour mixture and stir gently with a fork -- the dough should begin holding together. If the mixture still appears dry and crumbly, add the remaining water, 1 teaspoon at a time for the smaller quantity of dough, a tablespoon at a time for the larger quantity, until the dough holds together easily.
To mix the dough in the food processor, combine flour, salt and baking powder in work bowl fitted with metal blade. Pulse 3 times at 1-second intervals to mix. Cut butter into 1-tablespoon pieces and add to work bowl. Process, pulsing repeatedly at 1-second intervals, until the mixture is fine and powdery, resembles a coarse-ground cornmeal and no large pieces of butter remain visible--about 15 pulses in all. Scatter the minimum amount of water on the butter and flour mixture and pulse 5 or 6 times -- the dough should begin holding together. If the mixture still appears dry and crumbly, add the remaining water, 1 teaspoon at a time for the smaller quantity of dough,one tablespoon at a time for the larger quantity, until the dough holds together easily.
Turn the dough out onto a lightly floured surface and form it into a disk (two equal disks for the larger amount of dough). Sandwich the disk(s) of dough between two pieces of plastic wrap and press it into a 6-inch circle. Refrigerate the dough until firm, or until you are ready to use it, at least 1 hour.