For the parfait, place the sugar and the water into a heavy-based pan. Bring to the boil, then simmer for 2-3 minutes, stirring until the sugar has dissolved. Set aside.
Place the egg yolks into the bowl of a stand mixer and start whisking. Gradually drizzle in the sugar syrup while whisking continually. Once all of the sugar is incorporated, continue whisking for a further ten minutes, or until the mixture has thickened and has almost tripled in volume.
Remove the bowl from the mixer and gently fold in the whipped cream and the banana liqueur. Pour the mixture into four ramekins and chill in the freezer for at least two hours.
For the bitter chocolate ice cream, place the chocolate into a heatproof bowl set over a pan of simmering water (make sure the bottom of the bowl doesn't touch the water surface). Leave to melt completely, then remove from the heat and allow to cool for 2-3 minutes.
Whisk together the egg yolks and the caster sugar in a bowl until the mixture is pale and fluffy.
Bring the milk and the double cream to the boil in a heavy-based pan, then remove from the heat immediately. Pour a third of the milk and cream mixture into the egg yolk and sugar mixture, whisking continually, until well combined. Whisk in the remaining milk and cream mixture until smooth and creamy.
Return the mixture to a clean, heavy-based pan and cook over a low heat, stirring frequently, until the mixture thickens enough to coat the back of a wooden spoon. Allow to cool.
Pour the mixture into the bowl of an ice cream machine. Churn according to the manufacturer's instructions, then spoon the finished ice cream into a plastic container and chill in the freezer for one hour.
For the caramelised bananas, place the sugar into a heavy-based frying pan and cook over a medium heat for about ten minutes, or until the sugar has melted and caramelised (do not stir the sugar until it has melted).
Carefully add the rum to the sugar (it will spit) and stir until well combined. Remove the pan from the heat and add the bananas, turning in the mixture to coat. Transfer the bananas to a non-stick baking tray and allow to cool.
To serve, place a piece of caramelised banana on each of four serving plates. Quickly dip the ramekins in hot water to loosen the parfait from the sides, then turn out onto the plates next to the bananas. Serve with scoops of bitter chocolate ice cream on the side.