Grease a medium square cake tin (use one at least 2 inches deep) or a loaf tin. Cream the butter and sugar until light and fluffy. Beat in the eggs one at a time until combined, stir in the mashed banana. Combine the sour cream and milk, sift the flour and carb soda together. Fold in half the dry ingredients with half the sour cream and milk, then repeat with the remaining ingredients until smoothly combined.
Pour the mixture into the cake tin, make a slight well in the middle and bake at 325-350° for about 50 minutes. Test with a skewer and cook for a few minutes longer if not cooked through. Cool well before icing.
To make the icing, melt the butter and brown sugar in a saucepan, and heat stirring constantly without boiling for 2 minutes. Blend a few spoonfuls of the caramel mixture into the sour cream, then add the sour cream mixture to the caramel in the saucepan. Bring to the boil, stirring constantly, remove from the heat and stir in the icing sugar. Spread the icing on the cool cake.