Preheat oven to 325°F. Have the baked 9-inch pie shell ready.
In a large saucepan whisk together 1-1/2 cups sugar, 1/4 cup cornstarch and a dash of salt. Gradually whisk in 2-1/2 cups milk until smooth.
Cook the milk mixture over medium heat, stirring constantly, until it begins to thicken and bubble.
While the milk mixture heats, lightly beat the 4 egg yolks in a small bowl.
Temper the yolks: slowly whisk a small amount of the hot milk mixture into the yolks to warm them, then whisk the yolk mixture back into the saucepan. Continue cooking and stirring until the custard is thick and glossy.
Remove the saucepan from the heat and immediately stir in 1/4 cup butter, 2 Tbsp light corn syrup, 2 tsp vanilla extract and the 3-oz sweetened flaked coconut until fully combined.
Pour the hot coconut custard into the baked pie shell. Set aside while you make the meringue.
In a clean bowl, beat the 4 egg whites with 1/2 tsp cream of tartar and 1/4 tsp salt at high speed until soft peaks form.
With the mixer running, add the 1/2 cup sugar gradually, about 1 tablespoon at a time, and continue beating until stiff, glossy peaks form and the sugar is dissolved.
Spread the meringue over the warm custard, making sure to seal the meringue to the edge of the pastry crust so it touches the crust all around.
Bake the pie at 325°F for 25–28 minutes, or until the meringue is golden brown.
Cool the pie completely on a wire rack, then store it in the refrigerator.