Preheat the oven to 375 degrees F.
Adjust the rack to the center of the oven. Butter 2 (9-inch) round layer-cake pans. Line the bottoms with parchment paper. Butter the paper and dust all over lightly with flour. Set aside.
Sift together the flour, baking powder, and salt and set aside. In large bowl of electric mixer, beat the butter to soften a bit. Add the vanilla and sugar and beat for a few minutes. Add the eggs and milk and beat until smooth. On the lowest speed, add the dry ingredients in 3 additions, scraping the bowl with a rubber spatula as necessary, and beating only until smooth after each addition. Remove from the mixer and stir in the orange rind.
Divide the batter between the prepared pans. Tilt and shake the pans gently to level the batter. Bake for 25 to 30 minutes, or until the cakes come away from the sides of the pans and tops spring back when lightly touched.
Remove from the oven. Let stand for about 5 minutes. Cover with racks or cookie sheets and invert. Remove pans and papers. Cover with racks and invert again to cool right side up.
When the layers have cooled completely, place 4 strips of waxed paper or baking parchment around a cake plate, and place 1 layer on the plate, upside down. Spread with a thin layer of smooth preserves, reserving some for the second layer.
Make the Fluffy White Icing.
Spread 1/3 of the icing on the bottom layer. Sprinkle with 1/3 of the coconut. Put on the second layer, right side up, so that the 2 cake bottoms meet in the middle. Spread the top with the remaining apricot preserves. Use another 1/3 of the icing to ice around the sides of the cake. Use the remaining 1/3 of the icing to ice the top of the cake. Quickly spread with a long, narrow metal spatula to smooth the top and sides.
With the palm of your hand, press another 1/3 of the coconut onto the sides and sprinkle the remaining coconut evenly over the top. Remove the paper strips, pulling each 1 out by a narrow end.
Mix all of the ingredients except for the vanilla and almond extracts in the top of a large double boiler; it must have at least an 8 to 10-cup capacity. Place over hot water on moderate heat. Beat with an electric mixer at high speed for 5 to 6 minutes, until the mixture stands in peaks when the beaters are lifted.
Immediately, in order to stop the cooking, transfer to a the large bowl of an electric mixer. Add the vanilla and almond extracts and beat at high speed for about 5 minutes more, scraping the sides and bottom of the bowl almost continuously with a rubber spatula, until the mixture is smooth and very thick. Use immediately.
Fresh coconut, freshly grated, is a rare treat. If possible, use it. Fresh coconut is moist. If you use canned coconut, use the moist type and the most finely shredded.
Recipe courtesy Maida Heatter, from Maida Heatter's Book of Great Desserts