In a medium saucepan over medium-high heat, combine the well-stirred coconut milk, whole milk, shredded coconut, 1/3 cup of the granulated white sugar, and salt.
Bring the mixture to a simmer, stirring occasionally to dissolve the sugar.
In a separate medium mixing bowl, whisk together the egg yolks, remaining 1/3 cup granulated white sugar, and cornstarch.
Whisk until the mixture is smooth, fully combined, and free of lumps.
Gradually whisk the hot milk mixture into the egg yolk mixture to temper the eggs.
Continue whisking while adding the hot mixture slowly to prevent the eggs from curdling.
Return the tempered mixture to the saucepan.
Place the saucepan over medium heat.
Bring the mixture back to a simmer, whisking constantly.
Continue cooking until the filling thickens to a pudding-like consistency and a few bubbles burst on the surface, approximately 30 seconds after thickening.
Remove the saucepan from the heat.
Whisk in the vanilla extract and unsalted butter until smooth and fully incorporated.
Pour the warm coconut filling into the cooled graham cracker crust.
Smooth the top of the filling evenly.
Cover the pie with plastic wrap.
Press the plastic wrap directly against the surface of the filling to help prevent a skin from forming.
Refrigerate the pie for at least 3 hours, or until the filling is firm.