Preheat the oven to 350°F (175°C) and prepare three 8-inch cake pans by spraying with oil and lining the bottoms with parchment paper. Grease the parchment paper.

In a medium bowl, sift together the flour, cornstarch, baking powder, baking soda, and salt, then set aside.

Using a mixer, beat the butter for 30 seconds. Add the oil and sugar, and beat on medium-high speed until light and fluffy.

Add the egg whites one at a time, mixing well after each addition and scraping down the sides of the bowl as needed.

Add the coconut yogurt, vanilla, and coconut extract, and mix to combine.

Add half of the coconut milk, stir on low to combine.

Add half of the dry ingredient mixture. Mix just until combined, being careful not to over mix.

Pour in the remaining coconut milk, and stir.

Add the remaining flour mixture and mix on low.

Gently fold in the shredded coconut.

Evenly divide the batter between the prepared pans and bake for 25-30 minutes, or until a toothpick inserted in the center comes out clean. Let the cakes cool in the pans for 10 minutes before transferring them to a wire rack to cool completely.

If not assembling the cake on the same day, wrap each layer in plastic wrap and keep the layers frozen. Keeping the layers frozen will prevent them from drying out.

Place the sweetened condensed milk, butter, shredded coconut, and heavy cream (or coconut cream/milk) in a saucepan with a heavy bottom over medium heat.

Cook the mixture, stirring non-stop, for about 10 to 15 minutes, until thick, falling into chunks off the spatula.

When you run the spatula through the filling, you should be able to see the bottom of the pan.

Transfer the filling to a bowl, cover with plastic wrap and let it come to room temperature.

You can make it ahead of time and store in the fridge for up to 1 week, or freezer for up to 2 months. Let it come to room temperature on the counter before using as filling for the cake.

Place the butter in the bowl of a stand mixer, and beat on medium speed for 1 minute. Alternatively you can use a hand mixer.

Add the cream cheese to the bowl and beat with the butter for another minute.

Scrape the bowl and beat for another 30 seconds.

Add 4 cups of powdered sugar and mix on low until incorporated.

Add 2 tbsp of coconut milk and stir on low.

Add the remaining cup of sugar only if needed to make the frosting stiffer if it’s too runny.

Add the coconut extract and stir on low.

The frosting should be smooth and creamy.

Place some of the frosting in a piping bag lined with a round tip.

Place a cake layer on a cake plate.

Pipe a ring of frosting around the edges of the cake.

Fill the center about 1/3 cup to 1/2 cup of the coconut filling. Spread with an offset spatula to smooth it out.

Top with the other cake layer.

Repeat the process by piping the ring of frosting around the edges of the cake, and fill the center with the coconut filling.

Top with the final cake layer.

Spread the frosting on top and around the edges of the cake, use an offset spatula to smooth out the top and sides of the cake.

Use your hands to stick the shredded coconut on the sides of the cake, and on top of the cake too, covering the whole surface of the cake with the coconut.

Top the cake with the frosting and coconut truffles if desired.