Fresh Gingerbread with Lemon Icing

It's fall in Seattle, even if others are enjoying 80 degree weather still. It's cold and rainy and I have begun to crave apple pies, pumpkin anything and this gingerbread. I've programmed my daughter to love it as well.
I gladly give all credit for this to the lovely Nigella Lawson. This was the first recipe I tried 10 years ago when I bought her book How to Be a Domestic Goddess. I'm still working on my domestic goddessness, but this cake gets me a little closer every time. Yes, you use fresh ginger, but you can get it anywhere these days. You don't need the lemon icing, but it's tangy sweetness plays off the gingerbread.

For the gingerbread:
1/2 cup plus 2 tablespoons unsalted butter
1/2 cup plus 2 tablespoons brown sugar
3/4 cup plus 1 tablespoon light corn syrup
3/4 cup plus 1 tablespoon molasses
2 teaspoons fresh ginger, finely grated
1 teaspoon ground cinnamon
1 cup plus 2 tablespoons milk
2 large eggs, beaten to mix
1 teaspoon baking soda, dissolved in 2 tablespoons warm water
2 cups all-purpose flour
cake pan, approximately 12 x 8 x 2 inches, greased and lined with foil or parchment paper

For the icing:
1 tablespoons lemon juice
1/2 cup plus 2 tablespoons confectioners' sugar, sifted
1 tablespoon warm water

Preheat the oven to 325°F.

In a saucepan, melt the butter along with the sugar, syrup, molasses, ginger, and cinnamon. Off the heat, add the milk, eggs, and baking soda in its water.

Measure the flour out into a bowl and pour in the liquid ingredients, beating until very well mixed (it will be a very liquid batter). Pour it into the pan and bake for 3/4 - 1 hour until risen and firm. Be careful not to overcook it, as it is nicer a little stickier, and anyway it will carry on cooking as it cools.

And when it is cool, get on with the icing. Whisk the lemon juice into the confectioners' sugar first, then gradually add the water. You want a good, thick icing, so go cautiously and be prepared not to add all the water. Spread over the cooled gingerbread with a palette knife, and leave to set before cutting.