Set your oven to 350°F (175°C).
Lightly grease and flour an 11 x 7-inch rectangular pan, or line it with parchment paper for easy removal.
In a mixing bowl, whisk together the flour, sugar, baking powder, and salt. Stir well to ensure even distribution.
Add the softened butter, coconut milk, eggs, and vanilla extract to the dry mixture.
Using a hand or stand mixer, beat on medium speed for about 2 minutes until smooth and creamy.
Gently stir in the shredded coconut using a spatula or wooden spoon, ensuring it's evenly mixed throughout the batter.
Pour the batter into the prepared pan, spreading it evenly.
Bake for 25-30 minutes, or until a toothpick inserted in the center comes out clean.
Let the cake rest in the pan for 10 minutes before transferring it to a wire rack to cool completely.