Pre-heat oven to 175 °C (347 F) and line a 10 x 10 inch square (25cm square) cake tin with baking paper.
Place the softened butter, sugars and vanilla into a large mixing bowl and beat with a wooden spoon for a few minutes, until pale, soft and fluffy. An electric beater can also be used.
Add one egg and beat until the egg has incorporated into the mixture. Add the second egg and beat until combined.
Add the mashed banana and oil and stir to combine.
In a small bowl, combine the flour, baking powder, bicard soda and salt and stir to combine. Add half of the flour mix to the butter mixture and gently fold until combined.
Add half of the buttermilk and stir.
Add the remaining flour and fold, followed by the remaining buttermilk. Gently fold until just combined. If you are adding chopped walnuts, gently fold them into the batter.
Gently add the batter to the prepared cake tin and bake for 40-45 minutes (60 minutes for an 8 x 8 inch square tin), or until the cake has cooked through. You can test the cake by inserting a wooden skewer into the centre of the cake. If it comes out clean, with a few crumbs sticking, it is ready.
Transfer to a wire rack to cool.