Combine blackcurrants and granulated sugar in a small saucepan. There is no need to add any water as the berries should be juicy enough.
Bring to a boil, reduce the heat and simmer until reduced, about 5 minutes. Remove from heat and allow to cool slightly.
When cooled, purée the mixture and stir in the crème de cassis. Cover and chill in the fridge until needed.
Dissolve the arrowroot powder in 80 ml coconut milk and set aside for 15 minutes to thicken.
Stir the remaining coconut milk and caster sugar together in a saucepan over medium heat until the sugar dissolves.
Add the arrowroot mixture and, stirring continuously, bring the coconut milk to a boil. It will quickly thicken.
Remove from heat and stir in the vanilla extract. Chill in the fridge for a few hours.
Place bananas into a food processor and pulse until it is thick and creamy. This will take a few moments and it will go through several stages (big chunks, little chunks, etc.) before it gets there. Persevere.
When bananas are creamy, add the chilled coconut milk mixture and pulse until thoroughly combined. Check the bottom of the bowl to make sure no bananas are stuck to the bottom.
Transfer mixture to a freezer-proof container or, if your food processor base is plastic like mine, pop the whole thing into the freezer, covered with a tea towel.
Freeze for one hour and then pop the bowl back onto the processor base and process again. Repeat every hour for three or four hours until the mixture is thick, creamy and resembles a soft scoop ice cream.
Transfer half the ice cream mixture into a freezer-proof container, smoothing over the top. Pour over half the blackcurrant purée, top with the remaining coconut milk base and finish with a layer of the remaining blackcurrant purée.
Using a palette knife weave figure of eight lines through all four layers of the mixture, taking care not to over blend. You will end up with lovely blackcurrant ripples through the coconut milk base.
Freeze overnight. Allow to soften for ten minutes before serving dusted with icing sugar.