Mix together the lime juice and caster sugar in a bowl. Add the bananas, stir well to coat and leave for 5 minutes.
Roll the bananas in half the cornflour until well coated and set aside. Sieve the remaining cornflour and self-raising flour into a bowl. Add the coconut.
Whisk together the egg yolks and soda or sparkling water in a clean bowl. Add the flour mixture and whisk again, until the mixture forms a thick batter.
Fill a deep medium-sized saucepan one-quarter full of vegetable oil. Heat the oil to 180°C (350°F) or until a cube of bread turns golden in 10–15 seconds.
Dip the bananas into the batter and carefully place into the hot vegetable oil to deep-fry for 1–2 minutes, in batches, until golden brown. Carefully remove with a slotted spoon and drain on to kitchen paper. Keep warm on a plate in a preheated oven, 150°C (300°F), Gas Mark 2.
Serve immediately, dusted with icing sugar and drizzled with honey.