Preheat oven to 300°F. Butter a 2-quart casserole. In medium saucepan over medium heat, combine 3 cups milk and maple syrup. Heat until just boiling, then add butter. In bowl, combine cornmeal, ginger and allspice. Gradually stir cornmeal mixture into hot milk. Reduce heat to low and cook until thickened (coats back of spoon), about 5 minutes. Fold in cranberries or cherries.
Spoon mixture into prepared casserole and pour remaining milk over top of pudding. Do not stir. Bake until milk has been absorbed and top is golden brown, about 1 1/2 to 2 hours. Serve warm.