Set the oven to 350°F and coat the inside of a 9-inch pie plate with grease. Cover the bottom and sides evenly to help the pie release.
Use a large mixing bowl to beat the eggs until uniform. The yolks and whites should blend together without distinct streaks.
Whisk the sugar, flour, melted butter, vanilla, and salt into the beaten eggs. Work through any visible flour pockets until the mixture looks evenly combined.
Pour in the milk, then add the shredded coconut. The milk loosens the mixture considerably, while the coconut remains in visible strands.
Stir everything together and transfer the batter to the greased pie plate. Expect a thin, pourable mixture rather than a thick pie filling.
Bake for 40–45 minutes, checking the center with a toothpick for a clean result. The coconut surface should look golden, with the center showing only gentle movement rather than a liquid ripple.
Transfer the baked pie to a wire rack and leave it undisturbed for at least an hour. The custard firms as it cools, giving the wedges enough structure for slicing.
Cut and serve the pie warm, adding whipped topping if desired. The filling should feel tender and set beneath the chewy coconut surface.