How to Make It
Preheat the oven to 350°. Butter two 8-inch round cake pans and line the bottoms with parchment paper. Butter and flour the pans, tapping out excess flour.
In a small bowl, sift the cake flour with the baking powder and salt. In a small pitcher, combine the milk with the coconut milk. In a medium bowl, beat the butter at medium speed until creamy. Slowly add the granulated sugar and beat until light and fluffy, scraping down the sides of the bowl. Add the egg yolks and vanilla and beat until smooth. At low speed, add the dry ingredients in 3 batches, alternating with the milk mixture; beat until smooth.
In another bowl, using clean beaters, beat the egg whites at high speed until firm but not dry. Stir one-third of the beaten whites into the batter until smooth, then fold in the remaining whites until no white streaks remain.
Divide the batter evenly between the prepared cake pans and smooth the surfaces. Bake for 35 minutes, or until the tops spring back when lightly pressed and a toothpick inserted into the centers comes out with just a few moist crumbs attached. Let the cakes cool in the pans for 10 minutes, then turn them out onto a wire rack to cool completely. Peel off the parchment paper.
Using a sharp serrated knife, cut each cake into 2 even layers. Spread the raspberry jam between the cut layers of each cake and then reassemble. Place one cake on a serving plate, right side up. Tuck 4 wide strips of wax paper under the cake to cover the plate. Spread 1 1/2 cups of the Seven-Minute Frosting on the top and then center the second cake over the first. Spread the frosting liberally over and around the cake. Dust your hands lightly with confectioners' sugar and press the coconut onto the side of the cake. Sprinkle the rest of the coconut on the top. Let the cake stand at room temperature for at least 30 minutes before slicing.
To grate fresh coconut, crack open a whole coconut; discard the liquid. Place the coconut pieces on a baking sheet and bake at 350° for 5 minutes to loosen the flesh from the shell; let cool. Peel the brown skin from the coconut meat, then shred the pieces in a food processor using the fine grating disk.
Be sure the cakes are completely cool before cutting them into layers. To help reassemble the cake halves evenly after cutting and spreading them with jam, place two toothpicks on top of each other on the side of the cakes, one near the top and the other near the bottom. Slice the cakes in half between the toothpicks and spread the bottom layers with jam as directed by the recipe. To reassemble, simply replace the top layers, lining up the toothpicks.