1For the cake, preheat oven to 180°C (approximately 350°F.
2Grease a rectangular cake pan with butter and line the bottom with parchment paper.
4In a bowl, add softened butter and sugar and beat with an electric mixer until the mixture is creamy.
5Add agave syrup and eggs, one at a time, beating well between each addition.
6Add lime juice and zest and stir well. Add coconut milk and grated coconut, mixing into batter.
7Add flour and baking powder and mix just until smooth. Pour batter into prepared pan.
8Bake in preheated oven for 40-45 minutes.
9Cake is done when toothpick inserted in middle comes out clean.
10Allow to cool slightly. Remove from pan and prepare topping.
11For the icing, in a bowl, place powdered sugar, lime juice and milk.
12Mix well until mixture is white, smooth and shiny, without lumps.
13Spread on the warm cake. Let stand so that icing can solidify.
14Sprinkle top with toasted coconut flakes. (Toast them in a dry pan, watching carefully, so that they do not burn).