The oven needs to be preheated at 350 degrees Fahrenheit. keep aside a nonstick baking pan sprayed with cooking spray and which is lined with parchment paper. Combine the flour, baking powder, and salt in a sifter and put aside.
Cream with the butter and 3/4 cup sugar in the bowl of a standing mixer fitted with the paddle attachment, then add the egg yolks, coconut extract, and vanilla and beat on medium speed for about 3 minutes, or until the mixture becomes thick and pale.
Meanwhile, whisk the egg whites in a separate dish until firm peaks form, then put aside.
Toss half of the milk into the butter and egg yolk mixture, along with half of the dry ingredients, and stir just enough to combine (do not overmix). Add the remaining milk and dry ingredients, and stir everything together.
Gently fold the beaten egg whites into the batter, being careful not to deflate the egg whites.
Pour the batter into the pan and bake for 25 to 30 minutes, or until a toothpick inserted in the middle comes out clean.
Allow the cake to cool for about 20 minutes before transferring it to a serving plate (make sure the platter has high edges because the milk mixture will run out the sides as you pour it on top).
Use a fork to pierce the top of the cake and set it aside.
Whisk together the coconut milk, sweetened condensed milk, and evaporated milk in a large measuring cup. Slowly pour this liquid over the top of the cake, allowing it to soak into the soft sponge.
Set aside for 20 to 30 minutes to let the milk mixture to soak in completely before proceeding to make the whipped cream topping.
Add the heavy cream to the bowl of a standing mixer fitted with a whisk attachment and whisk to make soft peaks. Add the powdered sugar and beat until firm peaks form.