Preheat the oven to 175C / 350 F. Lightly grease 2 x 8-inch round cake tins with butter.
Combine the flour, baking powder and baking soda in a large bowl, then set aside.
Beat the butter and sugar together with an electric whisk until light and fluffy, then whisk in the eggs one at a time.
Beat in the yoghurt, bananas and peanut butter, then stir in the flour little by little with a wooden spoon until totally mixed in. Finally, fold the chocolate chips through the batter.
Divide the batter between the two greased tins, then bake for 35 to 40 minutes or until the cakes begin to pull away from the sides of the pan and a skewer poked into the centre comes out without raw batter on it. Let cool for a while, then turn out onto a wire rack to completely cool.
For the frosting
Whisk together the peanut butter, butter and vanilla, then whisk in the milk little by little.
Fold in about half the icing sugar and cocoa, then whisk until well combined. Whisk in the rest until the frosting is smooth and spreadable*.
When the cakes are completely cool, spread half of the frosting on the top of one, then place the other cake on top. Spread the rest of the frosting over the top of the cake, then decorate with peanuts (if using). Will keep in an airtight container for at least 4 days (possibly longer - never lasted that long!)
Frosting recipe slightly adapted from this recipe on Food.com.*Add more icing sugar if still too runny; add more milk if too thick.