Have a clean, medium-sized bowl near the stove.
In a medium saucepan, combine the sugar, cornstarch, flour and salt. Whisk in the milk and half-and-half. Whisk in the egg yolks, one at a time. If you are using vanilla bean seeds, whisk them in now. Put a medium-high heat under this mixture.
Cook the custard, whisking steadily, until it thickens and begins to boil. Take care to whisk the sides and the bottom of the pan to prevent lumps of custard from forming. Once it boils, cook the custard two or three minutes more, whisking constantly. Take the custard off the heat.
If you skipped the vanilla bean seeds and are using vanilla paste or extract, add it now. Add the butter. Stir til combined. Pour the custard into the bowl and lightly press a sheet a plastic wrap onto the surface. Chill fully, until the custard is thick enough to hold its shape when the pie is sliced. This can take 4-8 hours.
When you are ready to assemble the pie--ideally no more than 6-8 hours before you serve it--slice two of the bananas and spread them in the bottom of the piecrust. Spoon half the custard over them. Slice the other two bananas and layer them over the custard. Spoon in the remaining half of the custard, smoothing it over the pie to make sure all the bananas are fully covered.
In the bowl of a stand mixer, combine the heavy cream and powdered sugar. Beat until stiff. Spoon or pipe it over the top of the pie. Sprinkle cookie crumbs over the top. Chill until serving.