Special equipment: two 8-inch round pans

For the cake: Preheat the oven to 350 degrees F.

Sift together the cake flour, baking powder, salt and 3/4 cup of the granulated sugar in a medium bowl. Whisk together the milk, vegetable oil, vanilla extract, coconut extract and 7 egg yolks in a large bowl until well combined. Add the dry ingredients to the wet ingredients and whisk until well combined and smooth. With an electric mixer, beat the 9 egg whites and the remaining 3/4 cup granulated sugar in another medium bowl until they reach stiff peaks. Fold the egg whites into the batter until combined and the batter is a uniform color.

Pour the batter into two ungreased 8-inch round pans. Bake until the top springs back when lightly pressed, 25 to 40 minutes. Remove the cakes from the pan and cool on a cooling rack for 1 to 2 hours.

For the filling: Combine the strawberries, raspberries, granulated sugar and lemon juice in a large saucepan over medium heat and bring to a simmer. Cook about 10 minutes. Add the cornstarch, whisking constantly to avoid lumps; cook, stirring, until thickened, 3 to 5 minutes. Cool completely. Transfer to a blender and puree.

For the buttercream: Cream the butter and shortening with an electric mixer until smooth. Beat in the confectioners' sugar until completely incorporated. Stir in the vanilla and 1 tablespoon heavy cream and beat until smooth. Add the remaining tablespoon heavy cream if needed to reach a spreadable consistency.

To assemble the cake: Once the cakes are cooled, level each with a bread knife or cake leveler. Using a pastry brush, generously apply double-berry filling to the top of one cake. Then combine 1/4 cup filling with 1 1/2 cups buttercream; mix thoroughly and spread this over the first filling layer. Place the second cake, leveled-side down, on top. Frost as desired with the remaining buttercream.