Preheat the oven to 325. Lightly grease a 9 x 9 x 2-inch baking pan and line the bottom with a piece of parchment paper that has been cut to hang over two opposite edges by a couple of inches. This overhang will make removing the cake from the pan clean and simple.
Combine the butter, water, molasses, honey and brown sugar in a medium non-reactive saucepan and place over low heat. Stir the mixture frequently until the butter is melted, and all of the ingredients are well blended. Remove from the heat, pour into a large bowl and set aside to cool.
Meanwhile, sift together the flour, baking soda, salt, ginger, cinnamon, allspice and cloves, and set aside. When the molasses mixture feels just warm to the touch, add the eggs, one at a time, beating well after each addition. Add the milk and stir to combine. Fold the dry ingredients into the batter in four additions, using big, long strokes. Don't be concerned if you can't get all the lumps out--settle for most of them! Stir in the grated ginger.
Pour the batter into the prepared pan and bake in the center of the oven for 1 1/4 to 1 1/2 hours, or until the top of the cake springs back when touched and a cake tester inserted into the center comes out clean. Allow to cool for 15 minutes, then, using the overhang of parchment, lift the cake out of the pan and cool completely on a wire rack before cutting. Well-wrapped in plastic, this gingerbread actually improves with age. If stored at room temperature, it will have a sponge-cakey texture and will keep for about 4 days. Refrigerated, it becomes stickier, denser, and wonderfully chewy and will last at least a week. Allow the cake to return to room temperature before serving. This cake is fabulous warm, and the only adornment it needs is mounds of softly whipped cream.
Recipe courtesy of Regan Daley's "In the Sweet Kitchen" (Artisan, 2001)