Line a 12-section bun tray with paper cake cases. Peel and finely grate the ginger, working over a plate to catch the juice. Put the butter, caster sugar, eggs, flour, baking powder and vanilla extract in a bowl. Add the grated ginger, reserving the juice for the icing. Beat with a hand-held electric whisk for about a minute until light and creamy.
Stir in the sultanas and then divide the cake mixture between the paper cases.
Bake in a preheated oven, 180°C (350°F), Gas Mark 4, for 20 minutes or until risen and just firm to the touch. Transfer to a wire rack to cool.
Beat the icing sugar in a bowl with the ginger juice, making up with enough water to create an icing that just holds its shape. Spread over the tops of the cakes with a small palette knife. Decorate with the crystallized ginger slices.