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To make the cake, in a medium bowl, combine the oatmeal, butter, and boiling water, and stir to mix them together a bit. Set aside for 20 to 30 minutes.
Heat the oven to 350ºF, and generously grease and flour two 9-inch round cake pans, or one 13-by-9-inch pan.
In a medium bowl, combine the flour, baking soda, salt, and nutmeg, and stir with a fork to mix everything well. In a large bowl, combine both kinds of sugar with the eggs and vanilla, and beat with a mixer at medium speed for about 2 minutes, stopping to scrape down the bowl, until thick and light colored.
Stir the flour mixture into the egg mixture in 2 batches, beating just long enough each time to make the flour disappear. Mix in the oatmeal, stirring and folding to combine everything into a nubby but well-mixed batter.
Scrape into the prepared pans and bake at 350ºF for 25 to 30 minutes, until the cakes are golden brown, spring back when touched lightly in the center, and begin pulling away from the sides of the pans. Cool in the pans on wire racks or folded kitchen towels for 10 minutes. If you have used round cake pans, carefully turn out the cakes onto wire racks, turn top side up, and finish cooling. Or cool the cake in the large rectangular pan.
To make the frosting, in a medium saucepan, combine the butter, evaporated milk, and sugar, and place it over medium heat. Bring to a gentle boil, stirring now and then. Remove from the heat, and stir in the vanilla, pecans, and coconut. Beat well with a wooden spoon, a whisk, or a mixer on low speed, until you have a thickened, cooled frosting. Spread it between the two layers and then on the top of the cake. Or spread it over the top of the rectangular cake, and serve it in squares, right from the pan.