Preheat oven to 150 deg C, 300 deg F, Gas mark 2
Grease and line a 9 inch/23 cm cake tin.
Place the oil, eggs, flour, bicarbonate of soda,sugar and ground ginger into a large bowl and beat well.
Stir in grated carrot and stem ginger, mix thoroughly.
Pour the cake batter into a prepared tin and bake for about 2 hours until a skewer comes out clean when inserted.
Place on a cooling rack for about 10 minutes before turning out.
Leave to cool completely before icing.
For the icing:
Sift the icing sugar and beat in the butter until smooth.
Add the cream cheese and beat until it is well incorporated.
Beat for another 5 minutes until light and fluffy.
Spread or pipe the frosting onto the cake.