Teatime Coconut Layer Cake

Preheat oven to 325 degrees. Coat three 9-by-2-inch round cake pans with cooking spray; line with parchment paper. Set aside.

Sift flour, 1 3/4 cups superfine sugar, the baking soda, and 1/2 teaspoon salt into the bowl of an electric mixer fitted with the paddle attachment. Whisk together 3/4 cup water, the vegetable oil, egg yolks, and vanilla in another bowl. Add yolk mixture to flour mixture; mix on medium-high speed until smooth, about 2 minutes. Transfer to a large bowl; set aside.

Put egg whites and a pinch of salt into the clean bowl of the mixer fitted with the whisk attachment; beat on medium speed until foamy. Raise speed to medium-high; beat until soft peaks form. Gradually add remaining 1/2 cup superfine sugar; beat until stiff, glossy peaks form.

Fold one-quarter of egg-white mixture into batter with a rubber spatula. Fold in remaining egg-white mixture in 2 batches. Divide batter evenly among prepared pans. Bake until cakes are golden brown and spring back when pressed, 30 to 35 minutes. Invert cakes onto wire racks to cool; remove parchment.

Bring 1 cup water, the granulated sugar, a pinch of salt, and the cream of coconut to a boil in a small saucepan, stirring occasionally. Boil 1 minute; let stand.

Trim cakes level. Place 1 cake on a serving plate, and brush with 1/3 cup coconut syrup. Spread with 1 cup buttercream, and sprinkle with 1/3 cup sweetened coconut. Top with another cake. Brush with 1/3 cup syrup; spread with 1 cup buttercream, and sprinkle with 1/3 cup sweetened coconut. Top with final cake; brush with remaining 1/3 cup syrup. Refrigerate until firm.

Spread 1 1/4 cups buttercream over top and sides of cake. Refrigerate until buttercream is firm, about 30 minutes.

Spread 1 1/2 cups buttercream over top and sides of cake. Refrigerate until buttercream is very firm, at least 1 hour. Fill a pastry bag fitted with a 1-inch basketweave tip (such as Ateco #898) with buttercream. Holding bag perpendicular to cake, pipe sides in a back-and-forth motion, starting at bottom. Refill bag as needed. Sprinkle top with remaining 1/3 cup sweetened coconut and the unsweetened coconut shavings. Cake can be refrigerated up to 2 days; let stand at room temperature 20 minutes before serving.