Make custard: In a medium saucepan, whisk together sugar, starch, and salt. Add the eggs and yolks one at a time, whisking until smooth and no pockets of sugar-starch remain before adding the next. Whisk in vanilla bean paste, if using, and then, very gradually, whisking the whole time, pour in milk, then cream. Bring mixture to a simmer over medium heat, whisking the whole time. As the custard begins to bubble, it will thicken. Simmer for one minute, whisking. Remove from heat and stir in the butter until it is fully melted, then vanilla extract. Let cool for 5 minutes.
While custard cools slightly, lop off a few inches of banana and leave it unpeeled and set aside until needed for decoration. Peel and slice remaining bananas into the bottom of your cooled crust. For an extra-silky filling, pour and press the custard through a fine-mesh sieve, right over the bananas. If you don’t wish to sieve it, just spoon it in. Spread the custard into an even layer, press a piece of plastic wrap against the surface, and chill (in fridge or, again, outside) until custard is cool and set, 1 to 2 hours.
Finish assembling: In a large bowl, beat heavy cream with sour cream, if you wish, sugar and vanilla until soft peaks form. Spoon or dollop over cooled custard, or you can make starry blobs, as I did, with a big star tip set into the corner of a pastry or freezer bag. Decorate with remaining banana, peeled and sliced. Cut into big wedges and don’t be surprised if it doesn’t last.
Do ahead: Banana cream pie keeps for 4 to 5 days in fridge.