Preheat the oven to 180 C (350 F) standard / 160 C (320 F) fan-forced. Grease and line an 8-inch square pan with baking or parchment paper, ensuring two sides overhang.
In a large mixing bowl, add butter and sugars. Beat using an electric mixer on medium speed until pale and creamy. Add vanilla and eggs, and beat briefly until combined.
Add flour, baking soda, baking powder, cinnamon and salt to the butter mixture, along with buttermilk and mashed banana. Gently stir using a spatula or wooden spoon until just combined. Stir in walnuts.
Transfer to prepared pan and smooth the top. Bake for approximately 40-45 minutes or until a skewer inserted comes out clean.
Carefully transfer cake to a wire rack to cool completely.
To make the cream cheese frosting, add butter and cream cheese to a large mixing bowl. Beat with an electric mixer on medium speed for 2 minutes until smooth and creamy. Add vanilla and sugar and beat on a low speed to combine.
Turn mixer up to medium speed and continue to mix until frosting is smooth and creamy.
Spread frosting using a small spatula on cooled cake. Sprinkle chopped walnuts on top.
