Preheat oven to 300 degrees F.
Place milk in a saucepan and slowly sprinkle the cornmeal over it and whisk in. Cook on medium heat for 20 minutes, whisking occasionally to make sure it's not burning or sticking on the bottom of the pan. Whisk in the molasses, salt, ginger or lemon, and butter and pour into an 8-cup buttered casserole (or "pudding") dish. Bake for 1 1/2 to 2 hours until set. Serve with cream, whipped or poured.