Center a rack in the oven and preheat to 350 (F). Prepare a 6 x 3-inch round cake pan by spraying generously with cooking spray and lining the bottom with a parchment paper circle. Spray the parchment paper with cooking spray as well. Set aside.
In a medium bowl, whisk together 1 cup cake flour, 1/2 cup almond meal, 1 tablespoon desiccated coconut, 1 1/2 teaspoons baking powder, and 1/2 teaspoon kosher salt until well combined. Set aside.
In the bowl of a freestanding electric mixer fitted with a paddle attachment, combine 1/2 cup unsalted butter and 3/4 cup granulated sugar. Beat on medium-high speed until light, fluffy and doubled in volume, at least 5 minutes.
Once the mixture is light and fluffy, reduce the mixer speed to its lowest setting. Add 1 large egg and 1 teaspoon pure vanilla extract continue beating until fully incorporated.
With the mixer speed still on its lowest setting, add the dry ingredients (from the 1st step) in 3 parts, alternating with 1/2 cup coconut milk in 2 parts, starting and ending with the dry ingredients. Continue mixing until all the ingredients are just combined.
Bake in the preheated oven for 25 to 30 minutes, or until the cake is golden and a skewer inserted into the center of the cake comes out clean. The top of the cake should bounce back when gently poked. Transfer to a wire rack to cool completely before using a serrated knife to slice the cake into 2-inch cubes for the parfaits.