Pour 4 cups hot milk into the top of a double boiler and place over simmering water. Slowly stir cornmeal into milk and cook until thickened, about 20 minutes. Stir occasionally.
Preheat oven to 300 degrees F (150 degrees C). Grease a 2-quart round baking dish.
Whisk maple syrup, brown sugar, molasses, eggs, melted butter, salt, ginger, and cinnamon together in a bowl. Stir maple syrup mixture into cornmeal-milk mixture until thoroughly combined; pour into prepared baking dish. Pour 1/2 cup cold milk over top of pudding.
Bake until set but still slightly quivery on top, about 2 hours. Let stand 30 minutes before serving.