Preheat the oven to 180 C / 350 F
in a small oven-proof dish (about 500ml in capacity), break up the croissant into large, thin shards and layer this with the sliced banana
put the sugar and water in a heavy past pot and heat. Do not stir, and allow the sugar to melt and turn golden
once the sugar has melted to a golden colour, remove it from the heat and whisk in the cream (there will be a lot of spluttering but keep stirring)
when the cream is incorporated, add the milk (it will be quite runny now) and the rum or bourbon
add the beaten egg whilst whisking all the time and immediately pour over the croissant and banana
allow this to stand for 10 minutes and then bake for 20 minutes until golden brown