In a small bowl, stir oats into boiling water. Set aside to soak for 20 minutes.
Preheat the oven to 350 degrees F (175 degrees C). Grease an 8×8 inch baking pan.
In a medium bowl, cream together the white sugar, 1 cup brown sugar and shortening until smooth. Beat in the eggs one at a time. Sift in the flour, baking soda, salt and nutmeg; stir just until moistened. Mix in the soaked oats. Pour into the prepared pan, and spread evenly.
Bake for 35 to 40 minutes in the preheated oven, until a toothpick inserted into the cake comes out clean. Turn the oven to the broil setting and let it heat up.
In a small bowl, stir together the melted butter, 1/2 cup brown sugar, heavy cream, coconut and vanilla. Spread over the top of the cake. Broil for a few minutes, just until the coconut is lightly browned.