Roll dough on a lightly floured surface, transfer to a 9-inch pie dish, trim the crust to ½ inch larger than the dish, flute the edge, and refrigerate for 30 minutes.
Preheat the oven to 425F / 218C.
Line pie crust with a foil (covering the edges so they don’t burn), fill the pan with pie weights or dry beans and bake for about 15 minutes or until lightly browned, Then remove the foil and the weights and bake for a further 3-4 minutes. Allow to cool on a wire rack.
Combine milk, heavy cream, and sugar in a saucepan. Cook on medium heat, whisking until smooth and the sugar has dissolved. Cook until it begins to gently simmer then turn heat to low and let it simmer for another minute.
Combine egg yolks and cornstarch in a heatproof bowl, then slowly stream about ¾ cup of the warm milk mixture into the eggs.
Very, very, slowly, pour the egg mixture into the saucepan, making sure to whisk continuously. Keep whisking and cook for a few minutes more until thickened and bubbly.
Remove the pan from heat and add butter and vanilla extract. Then place plastic wrap onto the surface of the custard to avoid any skin forming and refrigerate for 30 minutes.
Slice two of the bananas and spread them out over the bottom of the pie crust. Then pour the cooled custard on top. Cover the assembled pie with plastic wrap and refrigerate for at least 4 hours up, to overnight.
When ready to serve, spread (or pipe) on whipped cream, slice the remaining bananas, place on top, and add white chocolate curls (if desired).