Preheat the oven to 180°C/Gas Mark 4. Grease a 20cm (8in) square cake tin and line with non-stick baking paper.
Cream the butter and sugar together until light and fluffy. Beat in the egg yolks, bananas and buttermilk. Add the flour, baking powder and sultanas and beat until smooth.
Whisk the egg whites until stiff and fold into the cake batter. Pour into the prepared tin and arrange the nuts on top. Bake for 1 hour or until a skewer comes out clean.
Leave to cool in the tin for 10 minutes before turning out. Cut into squares.