Preheat oven to 320°F or 160°c. Grease with non-stick cooking spray or line with parchment paper an 8 inch square baking tin. Set aside.
Add the melted butter and brown sugar to a large mixing bowl. Mix until the butter and brown sugar are well combined. Add the eggs, vanilla extract and mashed banana, and stir until well combined.
Add the flour and baking powder to the wet ingredients. Mix until just combined. Pour the blondie batter into the prepared baking tin. Bake for 20 minutes, or until the edges of the blondie have set but the center is still slightly soft. Allow to cool completely in the tin.
To make the brown sugar frosting, add the melted butter and brown sugar to a small mixing bowl. Stir until well combined. Add the powdered sugar and mix once again until well combined, adding milk if necessary to get a spreadable consistency. Spread over the cooled blondie, then slice into individual pieces.
Notes
If the frosting is too thick, add a little extra milk. If the frosting is too thin, add a little extra powdered sugar.