Step 1Cream butter and sugar. Add eggs and mix thoroughly.
Step 2Sift together flour, cream of tartar and baking soda. Add to butter mixture. Mix well. Add milk and coconut milk.
Step 3Line bottoms of 2 (8-inch) round cake pans with parchment paper and coat with nonstick cooking spray. Divide batter between pans. Bake cakes at 350 degrees until toothpick inserted in center comes out clean, 20 minutes. Cool in pans on rack, then remove.
Step 1Combine cornstarch with coconut milk and milk in small saucepan. Add sugar, egg yolk and coconut, and cook over low heat, stirring constantly, until thick, 5 minutes. Cool, about 1 hour. Spread between cake layers.
Step 1Boil sugar and water in saucepan without stirring until it threads from spoon or reaches 230 degrees on a candy thermometer. Beat slowly into beaten egg whites, then increase mixer speed to medium and beat until frosting-like in consistency, 2 to 3 minutes.
Step 2Spread on top and sides of cake. (Frosting must be used immediately or it will dry out.) Sprinkle coconut over top of frosting, pressing down lightly.