In a medium saucepan, whisk together 1-1/2 cups sugar, cornstarch, and a dash of salt. Gradually add in the milk while whisking to combine. Place over medium heat and cook, stirring constantly until thickened, about 10 minutes.
Temper the egg yolks by slowly adding a small amount of the hot mixture while whisking continuously. Stir the tempered yolks back into the saucepan.
Continue to cook for an additional 2 minutes, then remove from heat. Stir in the butter, corn syrup, vanilla extract, and coconut until smooth.
Pour the coconut filling into the baked pie shell and let cool slightly.
In a clean mixing bowl, beat the egg whites with cream of tartar and salt until soft peaks form. Gradually add sugar, beating until stiff peaks form.
Spoon the meringue over the coconut filling, spreading to the edges to prevent shrinking. Create peaks and swirls with a spatula.
Bake in a preheated oven at 350°F (175°C) for about 10-12 minutes, until golden brown.
Allow to cool at room temperature for at least two hours before slicing.