Preheat the oven to 350 degrees and make sure you have all the ingredients together.
Combine the coconut milk, butter, brown sugar, and vanilla extract in a saucepan and warm over medium heat.
Dissolve the sugar. Adjust the heat to prevent the coconut milk mixture from coming to a boil and constantly stir to avoid scorching. Add the rum and set the saucepan aside to cool.
Sift the flour, salt, nutmeg, cinnamon, and cornmeal together into a large mixing bowl. Stir to combine.
Pour the cooled coconut milk mixture very slowly into the dry ingredients.
Continuously stir with a whisk to prevent lumps. Don't over whip; you don't want to incorporate too much air.
Use a rubber spatula to scrape all of the cornmeal pudding into the buttered springform pan. Make sure to spread out the cornmeal mixture evenly. If you don't have a springform pan, you can use a well-greased pie pan or silicone pan instead.
If you are using raisins, sprinkle them evenly on top.
Put the pudding in the oven and bake for 20 minutes.
In a bowl, whisk together the coconut milk, brown sugar, and cinnamon for the sweet topping.
After 20 minutes, remove the pudding from the oven, and stir gently. Pour the sweet topping on top of the pudding.
Put the pudding back in the oven and cook for an additional 1 hour and 20 minutes.
Remove the baked pudding and let it cool in the pan for about an hour. Release the rim of the springform. It can keep wrapped in the fridge for 4 or 5 days.