Virgin coconut oil was used in this recipe, as refined coconut oil is less flavorful. Martha made this recipe in episode 506 of Martha Bakes.
Butter a 10-inch springform pan and line bottom with parchment. Preheat oven to 350 degrees. Combine flour and baking powder in a small bowl. Combine oils in a liquid measuring cup.
In a mixing bowl, whisk eggs on medium speed until combined. Gradually add 1/3 cup sugar, and continue whisking until tripled in volume and pale yellow, 3 to 5 minutes. Reduce speed to medium-low, and slowly add the oil mixture in four batches, alternating and ending with ¼ cup plus 2 tablespoons coconut milk, until combined.
Sift flour mixture over egg mixture. Using a rubber spatula, gently fold in flour mixture until just combined. Gently fold in desiccated coconut.
Pour batter into prepared pan and smooth top. Bake, rotating pan halfway through, until cake bounces back when lightly pressed in the center, 22 to 25 minutes.
Meanwhile, in a small saucepan, combine 1/4 cup water and remaining 1/4 cup sugar over medium heat and cook, stirring, until sugar dissolves. Let stand until cool.
In a blender jar, combine the sugar-water, yuzu and remaining 1/2 cup coconut milk; blend to combine.
Remove sides from springform pan and transfer to a wire rack to cool. Using a pastry brush, brush cake generously with yuzu syrup, wrap well in plastic and freeze for at least 1 hour or overnight.