This cake recipe highlights strawberries in their truest form by layering them with a thick, sweet frosting and moist yellow cake made from coconut milk.
Preheat oven to 350 degrees. Lightly grease bottoms and sides of two 9-inch round cake pans. Line bottoms of each pan with a round of parchment paper. Grease paper and dust each pan with flour, tapping out excess. Set aside.
Sift together flour, baking powder, salt and baking soda into a large bowl. Set aside. Combine milk and coconut milk. Set aside. Beat butter and sugar in the bowl of an electric mixer fitted with the paddle attachment 5 minutes or until light and fluffy. Add eggs, one at a time, with mixer on low speed, scraping down sides of bowl as necessary. Add vanilla. Alternately add flour mixture and milk mixture in several additions, starting and ending with flour mixture, mixing just until combined. Stir in shredded coconut.
Spread batter into cake pans and bake 40 minutes or until golden and cake tester inserted into center of cakes comes out clean. Cool on wire rack 10 minutes. Invert to cool completely.
Beat the cream cheese, butter, and vanilla with an electric mixer until blended. Add confectioners' sugar and mix on low until combined.
Place one cake layer on a cake plate or stand. If cakes have rounded top, gently trim with serrated knife to make flat. Spread a thin layer of frosting on cake layer and top with chopped strawberries, pressing to flatten and help strawberries stay in place. Place other cake layer on strawberries, with flat side up and press down gently to secure. Frost top and sides of cake with remaining frosting. Press toasted coconut evenly on sides of cake and top with concentric circles of sliced strawberries. If not serving cake immediately, refrigerate until ready.