Preheat the oven to 150°C (300°F).
In a bowl, beat the eggs with granulated and muscovado sugars, and lime zest until pale and foamy.
Blend 3 baked and peeled bananas into the egg mixture. Stir in the oil and melted butter until smooth.
In a separate bowl, combine flour, toasted coconut, and baking powder. Gradually fold into the banana mixture.
Pour the batter into a lined or greased and floured cake tin. Sprinkle with coconut and top with halved bananas dipped in lime juice.
Bake for approximately 55 minutes, or until a knife inserted comes out clean. Cool in pan for 5 minutes, then turn out onto a wire rack to cool completely.