Preheat the oven to 200°C fan forced. Grease a 5cm deep, 20x30cm (base) baking dish.
Cut the mango cheeks from the stones. Using a large spoon, remove the mango fruit from the cheeks and thickly slice crossways. Place into a large bowl. Spoon over the vanilla and sprinkle with the sugar. Stir gently to combine.
Melt butter in a saucepan over medium heat. Once the butter has melted, increase the heat to high and cook for 2-3 minutes, or until the butter starts to turn golden. Remove from the heat. Set aside to cool for 10 minutes.
Combine the almond meal, icing sugar and flours in a bowl.
In a separate bowl, lightly whisk the egg whites with a balloon whisk until they start to become frothy. Pour the butter then egg whites into to the almond mixture. Stir until well combined. Pour into the baking dish.
Spoon the mango mixture, including all the juices, evenly over the batter. Sprinkle with flaked almonds. Bake for 40 minutes or until golden around the edges and set in the centre. Stand for 15 minutes. Serve warm, at room temperature with cream or ice cream.