Preheat the oven to 350°F (175°C).
Generously grease a 9-inch pie dish with butter or non-stick spray.
In a large mixing bowl, whisk the eggs and granulated sugar until smooth and slightly frothy.
Add the melted butter, self-rising flour, whole milk, vanilla extract, and salt. Mix until evenly combined.
Stir in the shredded coconut until it is evenly distributed.
Pour the batter into the prepared pie dish.
Bake for 45 to 50 minutes, until the top is golden and a toothpick inserted near the center comes out clean.
Let the pie cool completely before slicing; the custard layers will continue to set as it cools.