Preheat oven to 180C/350F. Grease a 14cm x 21cm (51/2 inch x 81/2 inch) (top measurement) loaf pan; line base and sides with baking paper, extending the paper 5cm (2 inches) over the sides.
Sift flours into a large bowl; stir in sugar, desiccated coconut and banana, then combined eggs, oil and essence until just combined. Spread mixture into the pan; sprinkle shaved coconut on top, pressing down lightly.
Bake bread for 1 hour 20 minutes or until a skewer inserted into the centre comes out clean. Stand bread in the pan for 10 minutes, then transfer, top-side up, to a wire rack to cool.