Put the eggs, caster (superfine) sugar and milk into a bowl and whisk together.
Place a large frying pan over a low to medium heat and add two tablespoons of butter.
Dip the brioche into the egg mixture, and once the butter has melted, place the brioche into the hot pan.
Cook for one minute on each side until golden brown. Transfer the pieces to a warm plate.
Wipe the pan clean, then return it to the heat and add the remaining butter. Once the butter has melted, add the bananas, keeping them whole.
Cook until golden on one side, sprinkle with half the brown sugar, then flip the bananas over.
Sprinkle the remaining sugar over the top, add the cinnamon then pour in the banana liqueur and rum.
Flame to burn off the alcohol. Simmer for a couple of minutes until the butter and sugar turns into a sauce, then stir in the pecans.
Spoon the bananas and the sauce all over the brioche, then top with the whipped cream and ice cream.
• James Martin’s American Adventure by James Martin, photography by Peter Cassidy, is published by Quadrille, £25