Butter and line a 23cm square baking tin (or use a shallow roasting tin, approx 30 x 20cm). Heat oven to 160C/fan 140C/gas 3. Put the butter, sugar and treacle into a saucepan and heat gently for about 5 mins until the butter and sugar have melted. Stir in the milk. The mix should be just warm to the touch; if not, leave to cool a little longer, then beat in the eggs.
Mix the chopped ginger and dry ingredients together in a large bowl and make a well in the centre. Pour the melted mix into the well, then gradually draw the dry ingredients into the wet with a wooden spoon, until you have a thick, smooth batter.
Pour the batter into the prepared tin, then bake for 1 hr until risen and firm to the touch. Resist taking a peek beforehand; the cake will sink if the oven temperature drops too quickly before it's cooked through. Poke a skewer into the centre to check that it's cooked - it should come out clean. If not, give it 10 mins more and check again. Leave the cake to cool in the tin. Once completely cool, turn out of the tin ready for icing, or wrap well in cling film and keep in a cool, dry place for up to a week.
To make the icing, sift the icing sugar into a bowl and add the gingery syrup. Beat well until you have a smooth, runny icing. Once the cake has cooled, drizzle with icing and cut into squares. If you're planning to let the cake mature for a while, make the icing on the day you want to cut it.