Pre heat oven to 350F degrees.

Grease 1 (9-inch) round cake pans, then line it with parchment paper. Grease again and dust lightly with flour.

Combine the butter, sugar and egg yolks in a large bowl. Using an electric hand mixer, beat on medium-high speed for 3 to 5 minutes, until light yellow and fluffy. Add the vanilla and mix well. The mixture might look curdled. Don't worry, that's normal!

In a separate bowl, sift together the flour, baking powder and salt. With the mixer on low speed, alternate between adding the dry ingredients and the wet ingredients (milk and coconut milk), beginning and ending with the dry ingredients. Mix until just combined. Reserve.

In a separate bowl, beat the egg whites on high speed until stiff peaks form. Gently fold the egg whites into the batter until evenly blended.

Pour the batter into the prepared cake pan and bake in the center of the oven for 45 to 60 minutes, until the top is browned and a cake tester comes out clean.

While the cake is baking, make the "sauce" by whisking together the coconut milk and the sweet condensed milk. Mix until well combined. Reserve.

When the cake is baked, but still warm, remove from pan and cut it in half and moisten the bottom part with half of the "sauce". Place the top part on top of that and, using a toothpick, poke holes all over its surface. Then, pour the remaining sauce until the cake absorbs everything.

Sprinkle with the shredded coconut and refrigerate until cold, for at least 4 hours.

Serve chilled!