Pour the milk into a medium saucepan and place over medium-high heat. Heat almost to boiling point. Keep hot.

Put the 5 egg yolks into the mixing bowl of a stand mixer fitted with the whick attachment (or use regular egg beaters with a portable mixer). Beat at medium speed, gradually pouring in the cup of sugar. Raise speed to high and beat until mixture thickens and turns a very pale ivory color.

Beat in the flour. While still beating, gradually pour in the hot milk.

Pour and scrape contents of bowl back into saucepan. Set over medium-high heat and cool, stirring constantly with a whire whisk (or beating with a portable electric moxer). Scrape bottom of pan with a spatula frequently, to make sure mixture is not sticking and scorching. It will get lumpy, but smooth back out again. When mixture comes to boil, reduce heat to low and cook for 2 to 3 minutes, still stirring and scraping.

Remove from heat and beat in vanilla extract. Refrigerate until cold. (To prevent a skin from forming, top warm custard with small pieces of butter, or place a sheet of plastic wrap directly on top of custard.)

After pastry cream has chilled, slice the bananas and fold 2 cups of slices into the pastry cream. Turn into the pie shell and smooth the top.

In a chilled bowl with chilled beaters, beat the whipping cream and 2 tablespoons powdered sugar until just stiff. Spoon over the top of pie, or pipe into a pastry bag fitted with a star tip and cover pie with whipped cream stars. Refrigerate until ready to serve.