How to Bake Banana into Banoffee Pie

Banoffee pie is a no-bake dish but what you suggest could be achieved by constructing the dish as normal (biscuit base, covered in caramel and then sliced banana), then sprinkling lightly with sugar and browning under the grill.

Allow to cool, top with whipped cream and eat (ensuring to call emergency services before insulin coma sets in).

Alternatively, You could cook the bananas in a pan with sugar and butter, chop them up and mix with the caramel before constructing the pie.

My recipe, from the originators' Nigel Mackenzie and Ian Dowding cookbook, The Deeper Secrets of the Hungry Monk, has the bananas sliced, arranged over crust, and the caramel poured over the bananas. The only part that is cooked is the sweetened condensed milk and butter, boiled down to make the caramel.

Since we don't do recipes on SE, I've given you the Wikibooks link which has the full ingredients and directions.

I have seen a hot version of banoffee pie, made with bananas, and caramel, and marshmallows (since whipped cream doesn't bake well, and it gives a bit of the lighter, creamy flavor, and is also good toasted hot). So you can have a hot version of the pie, and specifically it is possible to have a pretty good banoffe pie with cooked banana, which is helpful in figuring out how a banana caramel might work.

You might get a similar banana and caramel mixed effect as your friend's description just by heating the bananas with the caramel, as the above version does, so the flavors meld. You might, depending on how it is layered and cooked, get some caramelization of the top of the bananas when the pie is being heated. I'm thinking if you layer carefully with bananas on top and use a broiler, since otherwise the crust (or caramel) might burn. Or you might cook the bananas separately, just pan fry them until they are caramelizing. Or else cook them with the caramel, or with regular milk and sugar (or condensed milk) so that the caramel forms with the bananas already being cooked into a filling, the same way caramelized apple tarts work.

Then once you have your banana caramel, you can fill your pie tart, heat (or even chill, whatever), add your creamy whatever to balance the taste (marshmallows, whipped cream, ice cream), and go for it.