Preheat the oven to 170°C. Grease and line an 8-inch round tin with baking paper and set aside.
In a large bowl, mix together the ground hazelnuts, caster sugar and plain flour, until well combined.
Add the cooled, melted butter to the dry ingredients and mix until you have a nutty, paste-like mixture.
In a large, metal bowl (I used a stand mixer, fitted with the whisk attachment), whip the egg whites until they have just reached stiff peaks. The whites should hold their shape, but not look too dry.
Add a large spoonful of the whipped egg whites to the nut mixture and mix in vigorously to loosen the mixture.
Add the remaining egg whites and fold in, using a large metal spoon, until no streaks remain and you have a thick, even batter.
Pour the batter into the prepared tin and level out the surface. Place into the preheated oven and bake for 30-35 minutes, until the surface is golden and a skewer inserted into the centre of the cake comes out clean.
Allow the cake to cool for 5-10 minutes only before removing from the tin and transferring to a wire rack to cool completely.
Once cool, dust liberally with icing sugar (if desired) and serve. You can serve the cake plain, or with an accompaniment: vanilla custard is traditional, but a spoonful of whipped cream and some fresh berries is also delicious. The cake can be stored in an airtight container at room temperature for about 4 days.