Preheat the oven to 170°C (340F) and butter a 20cm. (8") non-stick cake tin.
First, prepare the ginger. In a medium saucepan, combine the ginger, water, brown sugar and honey and bring to the boil. Simmer for 10 minutes then cool. Set aside.
Using an electric mixer, cream the brown sugar, white sugar and butter together until thick and creamy. Remove the bowl from the mixer and add the eggs, one at a time, beating well by hand after each addition.
Add the flour and milk and stir gently but thoroughly. Remove the ginger from the syrup and slice thinly, then add 3/4 of the ginger to the cake, stirring to distribute the ginger.
Pour the cake batter into the prepared tin and bake at 170°C (340F) for one hour, or until the cake appears firm and dry on top and yields gently to pressure when pressed in the centre with your finger. Pour the ginger syrup over the hot cake and allow the cake to absorb the syrup. When the syrup has been absorbed, remove the cake tin.
To serve, spoon some thick, pure cream on top of the cake and decorate with the remaining slices of ginger. Alternatively, serve the cream on the side of the cake, with the ginger slices folded through the cream or on top of the cake.