Preheat your oven to 350°F (175°C).
Grease and line three 6-inch round cake tins. If you don't have three cake tins, you can just use the same one and bake one third of the mixture at a time, but obviously this will take longer.
In the bowl of a stand mixer, mix together the flour, sugar and salt.
Add the softened butter, coconut milk, eggs, and vanilla extract to the dry ingredients.
Mix with a stand mixer or hand mixer on medium speed for about 2 minutes until well combined.
Gently fold in the shredded coconut by hand using a spatula or wooden spoon until evenly distributed.
Divide the batter evenly between the three prepared cake tins (or put one third into your cake tin).
Bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean.
Remove from the oven and let the cakes cool in the tins for about 10 minutes before transferring them to wire racks to cool completely.