Preheat oven to 180C and line 2 oven trays with baking paper. Beat together butter and sugar until light and fluffy (2-3 minutes). Sieve flour and cocoa over butter mixture and beat to combine. Add corn flakes and stir to combine. Place heaped tablespoonfuls of dough on prepared trays, press lightly to flatten and bake, swapping trays halfway, until edges are firm (10-12 minutes). Cool completely on trays.
For icing, combine icing sugar and cocoa in a bowl. Add butter and 1½-2 tbsp hot water and stir until smooth, adding a little extra water until mixture is thick but just spreadable. Spread thickly over biscuits and top with hazelnuts. Afghans are best eaten the day they’re made, but will keep for 2 days in an airtight container.