Make the sauce for the pie by putting the butter, sugar and double cream into a pan over a medium heat and stir frequently until everything melts; bring the mixture to the boil for just a minute; remove from the heat and allow to cool to room temperature – it should thicken and become spreadable
Preheat the oven to 200C/Gas6
Roll out the pastry and place on a baking sheet lined with baking paper; score a border all the way around the edge of the pastry 1 cm from the edges; prick the centre with a fork
Spread ¾ of the sauce within the border, set aside the rest to use later
Peel the bananas, cut into thin discs and arrange on top of the sauce, overlapping so they all fit; glaze the pastry border with the beaten egg
Bake for 35 minutes until the pastry is crisp underneath and the bananas have darkened; don’t worry if the pastry has really puffed up because it will sink back on cooling; cool on the tray
Whisk together the cream, icing sugar and vanilla extract to soft, floppy peaks, chill
When the pie is cool, randomly dollop with cream, warm the sauce just until runny and drizzle it over the top; scatter the chopped banana chips on top
8 servings