In a bowl, combine the flour, sugar and salt. Use a pastry cutter to cut the cold butter in until the pieces of butter are no bigger than peas. Stir in the milk.
Dump the mixture out onto a clean work surface, and use your hands to gather the crumbs together. Keep gathering and pressing the crumbs together until it comes together into a ball – this should only take a minute or two. Use your bench scraper to scrape all the bits of dough off the work surface, if any of it sticks.
Lightly flour your work surface, the ball of dough, and your rolling pin. Roll the dough out, using using your bench scraper to loosen the dough from your work surface, and sprinkling more flour as needed to keep it from sticking, into a rough circle about 1/4 inch thick. There may be a few cracks in the dough, and you should see visible chunks of butter throughout.
Fold the dough into thirds, like a letter, and then in thirds again, so you have a neat little package of dough. Now roll it out again, large enough to fit into your pie pan with a little overhang. At this point, you can use the dough right away, or wrap it in plastic and refrigerate for up to 3 days, or freeze for 3-6 months.
Roll it out again, large enough to fit into your pie pan with a little overhang. Fit the dough into your pie pan, taking care not to pull or stretch the dough. Fold the edges under and crimp the dough all around the edge.
Use a fork to lightly prick the bottom of the dough - this is called "docking" and helps prevent the crust from puffing up as it bakes.
Freeze the dough in the pan for 30 minutes.
Preheat the oven to 400 F.
Lightly spray a piece of aluminum foil with non-stick spray, and fit it inside the frozen crust. Fill the foil with pie weights or dried beans.
Bake on the center oven rack for 15 minutes. Remove the pan from the oven, and gently remove the weights and foil. Brush the dough with the egg white, then return the crust to the oven (uncovered). Bake for an additional 12-15 minutes, until the crust is golden brown and cooked through.
Set aside to cool slightly.
Combine the milk and sliced bananas in a saucepan. Over medium heat, bring the milk to a simmer. Remove from the heat.
Pour the milk with the bananas into a lidded container, and refrigerate for 12 hours (overnight) to infuse the milk with banana flavor.
After 12 hours, strain the milk and discard the bananas.
In a saucepan, whisk together the sugar and corn starch. Whisk in the cream and egg yolks until smooth, then whisk in the banana-infused milk and the vanilla bean seeds.
Over medium heat, whisk the custard constantly and bring it to a boil. It should take about 10-12 minutes of whisking before it begins to boil and thicken. Once this happens, continue to cook, whisking constantly, for 1 full minute, until the custard is very thick.
Remove from the heat and whisk in the butter until smooth. Pour the custard through a mesh strainer to remove any bits of cooked egg. Let the custard cool at room temperature, uncovered, for about an hour, until it's no longer steaming hot.
Stir up the custard and spread it into the baked crust. Refrigerate for about 2 1/2 - 3 hours, until chilled and set.
With an electric mixer, whip the cream until it starts to thicken. Add the powdered sugar and vanilla, and whip until soft peaks that hold their shape form.
Spread the whipped cream on top of the banana custard. If desired, garnish the top with sliced bananas, toffee bits or shaved chocolate. Banana cream pie is delicious served with salted caramel sauce or chocolate syrup.
Loosely cover the leftover pie, and refrigerate for up to 3 days.