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Heat oven to 180C/160C fan/gas 4. Oil and line the bases of 3 x 20cm sandwich tins with baking parchment. Mix the flour, cinnamon, baking powder, half the sugar and the coconut in a large mixing bowl. In another bowl mix the beaten whole eggs, mashed bananas, grated carrot, drained crushed pineapple, milk and oil. Beat the egg whites until stiff, then add the remaining sugar and beat until stiff and shiny again.
Stir the wet mixture into the dry until smooth and lump-free, then using a large metal spoon or spatula, fold in the egg white mixture. Divide evenly between the tins and bake for 25 mins until risen and a skewer comes out clean. You might need to swap the position of the tins after 20 mins.
For the drizzle, scoop out the passion fruit pulp into a small pan. Add the pineapple juice and caster sugar and heat until bubbling, then bubble until syrupy. For the icing, beat the cheese and butter until lump-free, then beat in icing sugar and vanilla. Chill until ready to assemble.
Poke the cakes all over with a skewer, drizzle over most of the passion syrup, then cool. Once cool, spread the icing over two of the sponges. Sandwich together and top with the third, un-iced, sponge. Drizzle over the remaining syrup.