Preheat oven to 375F and position rack in center of oven. Line an 8x8 inch cake pan with parchment paper. Coat parchment paper and pan sides lightly with oil.
Whisk dry ingredients together in a large bowl to blend well. Whisk wet ingredients (except cider vinegar) together in small bowl to blend well, then whisk into the flour mixture until well blended. Whisk in the cider vinegar.
Transfer cake batter to prepared pan and bake until tester inserted into center comes out clean, about 35-40 minutes. Cool cake completely in pan on rack, about 1 hour. Turn cake out onto platter, peel off parchment paper.
Whisk together the soaking syrup ingredients, and then brush over top of cake.
For the frosting, combine all ingredients in a high speed blender and blend until smooth. Pour into a bowl, and place in the freezer for about 30-45 minutes (whisking every 15) until it thickens to the consistency of thick whipped cream. Spread the frosting over cake, then top with large flake coconut (and rose petals, if using).