Preheat the oven to 180°C and lightly grease a medium loaf tin or two small silicone bread moulds.
Mash the banana in a bowl, then add the egg, honey and vanilla. Mix well until smooth.
Stir in the oats, mixed spice and self-raising flour, mixing just until combined.
Gently fold in the chopped chestnuts and dates.
Spoon the batter into the prepared mould(s), smoothing the top.
Bake for 20 minutes for small moulds, or 30–45 minutes for a single larger loaf, until cooked through and a skewer inserted into the centre comes out clean.
Allow the cake to cool before serving.
To serve: Dust with icing sugar, or for a richer treat, spread with a light cream cheese frosting.