Preheat oven to 350 degrees. Place racks in middle of oven. Lightly grease three 8-inch-round cake pans and line each pan with parchment paper circle.
Sift together flour, baking powder, cream of tartar and salt in mixing bowl. Set aside.
Cream butter in large mixing bowl for 1 minute, using mixer on medium speed. Continue beating, gradually adding sugar, and beat for 3 to 4 minutes, scraping down sides of bowl. Blend in egg yolks, one at a time, mixing well after each.
Add vanilla extract and 1/4 cup of soymilk and beat on low for 1 minute.
Using rubber spatula, and stirring by hand, add flour mixture and remaining soymilk in separate batches, starting and ending with flour. Beat lightly between additions, until ingredients are well blended. Beat egg whites until stiff and fold them into batter.
Pour batter into prepared pans, dividing equally among pans. Smooth tops with rubber spatula.
Bake for 22 to 25 minutes, or until top of cake springs back when lightly touched in center. Remove pans from oven and cool on rack for 10 minutes. While oven is still hot, toast coconut flakes: Place flakes on cookie sheet and bake at 350 degrees for 7 minutes, or until flakes turn golden. Watch coconut closely because flakes can burn easily. Remove from oven and cool.
Slide thin knife around layers to detach them from pans. Invert cakes and peel away paper liners. Let layers cool, right-side up on racks, for at least 1 1/2 hours.
Meanwhile, to make Coconut Custard Cream, combine sugar, cake flour, coconut cream powder and salt in large saucepan. Whisk in 1/2 cup soymilk and beat until smooth. Whisk in remaining soymilk.
Cook over medium-low heat about 5 minutes, whisking gently but constantly until thickened. Cook 2 minutes more or until mixture loses its floury taste. Stir in vanilla extract and coconut.
Pour custard into small bowl. Smooth top with rubber spatula and cover surface with wax paper. Refrigerate until cooled.
To make White Frosting, place sifted confectioner's sugar, butter, salt, vanilla and soy creamer in bowl of electric mixer fitted with beaters. Set mixer on low speed to prevent sugar from billowing out of bowl and beat for 2 minutes. Increase speed and beat until smooth and creamy. Add more soy creamer, if needed, to make frosting spreadable.
To assemble cake, put one layer on serving plate and ice with half the pastry cream. Add second layer and ice with remaining pastry cream. Place third layer on top. Cover sides and top of cake generously with frosting. Sprinkle with toasted coconut, covering sides and top of cake.
This recipe yields 8 to 10 servings.
Per Serving: 820 Cal; 9g Prot; 35g Total Fat (17 Sat. Fat); 120g Carb.; 115mg Chol; 470mg Sod.; 3g Fiber.