Preheat the oven to 170C/325F/Gas 3. Line the base and sides of a 20cm x 12cm/8in x 5in loaf tin with baking parchment.
Beat the butter and sugars until light and coffee-coloured. This is best achieved in a food mixer.
Toast the hazelnuts, rub them in a tea towel to remove their skins, then grind quite finely.
Slowly add the eggs to the butter and sugar mixture, then mix in the toasted ground hazelnuts and self-raising flour.
Peel the bananas and chop them the small pieces. Gently fold the vanilla extract, the bananas and the chocolate chips into the cake mixture, turning gently and taking care not to overmix.
Scoop the cake batter into the prepared loaf tin. Dust with a little demerara sugar. Bake for between 1 hour and 1 hour 10 minutes, covering the cake with foil if the top starts to darken too quickly.