Peel 4 of the bananas and purée using an immersion, stand blender or food processor.
In a large, heavy-duty saucepan over set medium heat whisk together the milk, cream, sugar,cornstarch and salt. Continue whisking until it comes to a simmer and begins to thicken.
Remove the pan from the heat and whisk in banana purée then the butter and lastly the egg yolks. Return to the heat, continue whisking and bring back up to a simmer. Cook 3 to 5 minutes longer.
Optional but recommended step for super creamy pudding: Strain the pudding in batches through a wire strainer into a bowl set inside a larger bowl filled with ice.
Once all the pudding is strained add vanilla and whisk 2 minutes. Place a piece of plastic wrap or parchment on top of the pudding (touching) and refrigerate 3 hours or until well chilled.