Preheat the oven to 325 F fan assisted. Butter and dust with flour a 9" or 10" cake pan.
Beat the eggs for 5 minutes until they double in volume. Then add the condensed milk, the melted butter, the sifted flour and baking powder. Mix gently with a spatula until the mixture is even, without any lumps. (Or use your Kitchenaid, doubling the egg volume first) Pour the mixture into the cake pan and bake for 30-35 minutes.
As soon as it comes out of the oven, make tiny holes all over the dense cake using a fork and pour the mixture of coconut milk and sugar evenly over it.
Let it cool in its pan for about 5 min, then transfer it to a rack. Sprinkle it with grated coconut before serving. Fresh grated coconut is preferable, but you can use dried. Let the cake sit a few hours in the refrigerator after it cools.
*note: if you use some sweetened coconut milk or cream, your result will be sweeter.