In a medium saucepan combine milk, sugar, cornmeal, molasses, cinnamon and ginger. Stir over medium heat until thickened about 10-15 minutes. It should be thick but still pourable.
Stir in butter and vanilla and pour into a 1 quart baking dish.
Bake for 60-75 minutes until the center no longer moves when the dish is shaken. Let cool 10 minutes.
Serve while warm with vanilla ice cream or whipped cream if desired.