Step 1: Preheat oven to 350 degrees.
Step 2: Sift together cake flour, 1/3 cup sugar, salt and baking powder. Set aside.
Step 3: Combine egg, water and oil; add to sifted ingredients. Mix batter until smooth.
Step 4: In a separate bowl, whip egg whites with cream of tartar.
Step 5: Gradually add 1/4 cup sugar; continue to whip to form a stiff meringue. Fold batter into meringue and mix thoroughly.
Step 6: Pour into an ungreased 9-inch cake pan and bake about 30 minutes.
Step 7: Invert cake onto a rack and cool.
Step 8: Scrape vanilla bean seeds into milk and bring to a boil over moderate heat (add vanilla bean pod to milk as well).
Step 9: Combine sugar, flour and egg yolks; whip until light yellow.
Step 10: Slowly pour 1/3 of the hot milk into the egg mixture to temper it.
Step 11: Add milk-yolk mixture back into the remaining milk and cook over moderate heat, stirring constantly until thick. Immediately remove bean pod and strain, then place in a bowl and cover with plastic wrap. Chill.
Step 12: Whip cream and sugar until fluffy.
Step 13: Fold 1 cup into pastry cream; reserve the rest to frost cake.
Step 14: Cut cooled cake into three layers.
Step 15: Stir 3/4 cup of coconut flakes into pastry cream.
Step 16: Spread cream between layers of the cake.
Step 17: Frost top and sides of cake with remaining whipped cream and sprinkle with remaining coconut flakes.
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