1. Start by splitting a vanilla bean lengthwise and scrape out the seeds. Add both the seeds and the vanilla pod to a saucepan with milk and heavy cream. Set aside the seeds for later.
2. In a large bowl, whisk together sugar and cornstarch. Then mix in egg yolks and the reserved vanilla bean seeds, whisking until the mixture is smooth and lightens in color.
3. Heat the milk and cream mixture on medium until it’s almost boiling—watch for small bubbles forming around the edges.
4. Remove the saucepan from heat and discard the vanilla pods. While whisking, slowly drizzle a scant cup of the hot liquid into the egg yolk mixture to temper the eggs, preventing them from curdling.
5. Slowly whisk in the remaining hot liquid until smooth. Return the mixture to the stovetop and cook over medium heat, whisking constantly until it thickens to a pudding-like consistency.
6. Be cautious to adjust the heat to avoid scorching. Once thickened, remove from heat and stir a few times until it cools to about 140º.
7. Transfer the mixture to a food processor, adding butter. Pulse until the butter melts, and the custard is smooth and glossy.
8. Pour the custard into a bowl set over ice water, stirring occasionally until cool. I like to fill my sink partway with ice cubes and water to speed up the process. Once cool, cover the surface with plastic wrap and refrigerate for at least three hours.
9. After the custard has chilled, scrape about half into the prepared pie crust. Arrange banana slices on top, then spoon the remaining custard over them.
10. In a separate bowl, whip heavy cream with powdered sugar until soft peaks form. Top the pie generously with the whipped cream. Slice and enjoy your homemade Banana Cream Pie!