• Preheat the oven to at 350 °F. Butter and flour a 10" tube pan or Bundt pan. Combine 3 large eggs, 4 large yolks, 1 teaspoon vanilla extract and half the coconut milk in a small bowl, whisk to combine and set aside.
• Sift together 8 oz cake flour, ¼ teaspoon table salt1 teaspoon baking powder in a mixing bowl. Add 10 oz granulated sugar to the flour and mix at low speed for 30 seconds. Add 9 oz unsalted butter to the flour and mix until combined. Add the other ½ of the coconut milk and increase the speed to medium high. Mix for a full 2-3 minutes. The batter will lighten in color and texture. If your using a hand mixer add another minute or two to the mixing time.
• Scrape the bowl and beater thoroughly. On low speed, add the egg mixture in 3 increments, scraping the bowl after each addition. Mix just until the eggs are incorporated.
• Pour 3/4 of the batter into the prepared pan and smooth to an even layer. Sprinkle 4 oz sweetened coconut flakes over the batter, trying not let it touch the sides or middle of the pan. Dollop the remaining batter over the coconut and spread to cover the coconut.
• Bake until a toothpick inserted in the middle comes out clean (about 35 minutes).

Finish the Cake

• To make the coconut syrup combine 2 oz granulated sugar and 2 oz water in a small saucepan and heat over medium high heat until all the sugar is dissolved. Remove the syrup from the heat. Add a tablespoon of rum and half the coconut milk then set aside to cool.
• To make the coconut glaze, in a small bowl, combine 8 oz confectioner sugar with the remaining rum and coconut milk. Whisk until smooth.
• As soon as the cake comes out of the oven, pour the coconut syrup over the the top of the cake. Cool the cake in the pan for 20 minutes, then turn it out onto cooling rack set over a clean sheet pan. Allow to cool another 10 minutes until it is slightly warm.
• Pour the coconut glaze over the top of the slightly warm cake. Allow the glaze to drip down the middle and sides of the cake. Sprinkle the shredded coconut onto the glaze before it sets.
• Cool completely to allow the glaze to set then transfer to a serving plate. The cake keeps at room temperature, covered, for 2-3 days.