In a missing bowl mix the oil and sugar with electric mixer until smooth. Add egg yolks one at a time, beating after each addition.
Sift the flour, baking powder, salt, cinnamon and nutmeg together. Add the flour mixture to the oil and egg mixture and mix. Add Vanilla. Fold in the grated sweet potatoes.
In a separate bowl, beat the egg whites until they are stiff and from peaks. Gently fold the egg whites into the batter until blended.
Prepare three 9" cake pans by lining the bottoms with parchment paper or wax paper and spraying them well with nonstick baking spray. The type contains flour works best. Take my advice and do not skip this step! This cake is very moist and can stick or the layers can break if you do not line your pans. Pour the batter evenly among the pans and bake for 25 to 30 minutes. A pick inserted in the center should come out clean.
Remove from oven and allow to cool before turning onto a cake plate.
Prepare frosting when the cakes have cooled by combining the evaporated milk, sugar, butter, egg yolks and vanilla in a saucepan over medium heat. Cook for 12 minutes, stirring constantly or until the mixture has thickened.
Remove from heat and add coconut. Beat until cool and thick and spreading consistency.
Stack cake layers on a cake plate and frost between layers, top and sides. Garnish the top with the nuts. This frosting sort of runs down the sides of the cake and you can spread it around the sides. The consistency will be similar to the frosting on a German Chocolate Cake.