Food writer Nancie McDermott bases this yellow layer cake on a family favorite that her grandmother always served at Christmas.
Heat the oven to 350º. Grease and flour two 9-inch round cake pans and set them aside.
In a medium bowl, sift together the flour, baking powder, and salt.
In a large bowl, beat the softened butter with an electric mixer until creamy, about 1 minute. Add the sugar gradually, stopping to scrape down the sides of the bowl once or twice, until the mixture is fluffy and fairly smooth, about 2 minutes. Add the eggs, one by one, beating well each time, until you have a thick, smooth batter.
Add about one third of the flour mixture to the batter and beat well. Stir the vanilla into the milk, then add about half the milk to the batter and beat well. Continue beating as you add another third of the flour mixture to the batter, followed by the rest of the milk, and then the remaining flour mixture, until the batter is very thick and smooth. This should take a total of about 2 minutes mixing time.
Quickly scrape the batter into the prepared cake pans, dividing it evenly. Bake until the cakes are golden, and a toothpick inserted in the middle comes out clean, about 30 to 35 minutes.
Remove the cakes from the oven, allow them to cool for 10 minutes, and then turn them out onto wire racks or plates and let them cool completely.
To make the icing: In the top of a double boiler, or in a heatproof medium bowl, combine the sugar, corn syrup, water, egg whites, salt, and cream of tartar and beat on high speed with a handheld electric mixer, about 1 minute.
Bring the water to an active simmer in the bottom of the double boiler or the saucepan, then beat the icing at medium speed until the mixture is opaque white and foamy, about 1 or 2 minutes.
Increase the speed to medium-high and beat until the icing becomes white, thick, and shiny and triples in volume, about 7 minutes. Continue beating until the icing forms firm peaks and loses a little of its shine.
Remove the icing from the heat, add the vanilla, and beat for 2 minutes more.
Completing the cake: Place 1 cake layer topside down on a cake stand or serving plate, and cover it with the jam spread to within 1/2-inch of the edge. Use a rubber spatula to carefully spread 1 cup of the icing over the jam, then sprinkle about ½ cup of coconut on top.
Place the other layer on top of the iced layer with the topside up. First ice the sides, to help keep the cake steady, and then spread icing generously over the top.
Put the cake stand on a cookie sheet (to catch any loose coconut) and sprinkle coconut all over the cake. Gently pat handfuls of coconut onto the sides and top of the cake to cover any bare spots. Serves 18.