Preheat oven to 350 degrees F. Combine cornmeal and syrup in the top of a double boiler. Stir in hot milk. Cook mixture in top of double boiler over 2 inches of simmering water. Stir constantly for about 20 minutes, until thick and smooth. Remove from heat, remove top of boiler and stir in butter, spices, and salt. Add eggs and beat well. Pour mixture into a generously buttered 1-1/2-quart baking dish. Place baking dish in larger pan and pour about 1 inch of boiling water into larger pan.
Bake for about 30 minutes then stir. Continue baking for another 1-1/2 hours or until set. Serve warm with apple topping and heavy cream. For the apple topping, place the apples into a pan with the butter. Combine the sugar, cinnamon, and nutmeg, and sprinkle the mixture over the apples. Cook over medium-low heat for about 5 to 8 minutes, until the apples are soft. Stir constantly so that the apples don't turn brown or stick.