Lightly butter a 9 x 13 inch cake pan / baking dish and preheat the oven to 175C / 350F (170C / 340F fan oven).
In a food mixer or food processor (or in a bowl with a hand-held electric whisk), soften the butter (about a minute), then add the sugars and cream together until light and fluffy (about 2 minutes).
With the motor / whisk running, add the eggs one by one until combined, then whisk in the mashed banana, vanilla, and milk.
In a separate bowl, sift the flour together with the baking powder, baking soda, salt, and cinnamon.
Slowly add the flour mixture to the wet ingredients (pour wet mixture into a bowl if you’ve used a food processor), mixing until just combined.
Pour the batter into the cake pan / baking dish and bake for 30 minutes or until a skewer inserted into the centre of the cake comes out pretty clean. Leave to cool in the pan.
Meanwhile, make the frosting. Combine the butter, milk, peanut butter and vanilla in a saucepan and heat and stir until melted together.
Slowly add the powdered / icing sugar until you have a smooth and thick frosting. Pour over the cake and spread evenly.
Sprinkle over the chopped peanut butter cups (if using). Pop the whole pan in the fridge or freezer for a short while to set the frosting a bit, then slice and serve.