Preheat the oven to 375 degrees F. Bake the crust per the package instructions and cool the pie crust completely.
To make the coconut custard filling, whisk the egg yolks and cornstarch together in a large bowl OR in a stand mixer with the whisk attachment. (my preference since it will free up your hands to pour the hot liquid in later). Set aside. In a large saucepan, whisk the coconut milk, half-and-half, granulated sugar, and salt together over medium heat. You want the sugar to dissolve into the mix. Bring the mixture to a boil. Boil for 2 minutes, then reduce temperature to medium-low heat.
Using a measuring cup,remove about 1/2 cup of the mixture and, in a slow and steady stream, whisk into the egg yolk and cornstarch mixture while the stand mixer is on low. If whisking by hand, be careful that you aren't splashing the hot liquid. Keep whisking to prevent the eggs from scrambling. You are basically warming up the eggs and bringing them to temperature so they won't scramble when you add them back to the hot pot on the stove.
Once incorporated, take that mixture and add it into the hot mixture in the pot on the stove. Add in a slow steady stream whisking as you pour.
The custard will immediately begin to thicken. Whisk and cook for 1 minute - 2 minutes. If you notice any lumps or small pieces of egg, strain the mixture through a fine mesh strainer into a bowl. Use a spatula and press the mixture through the strainer. That will make the custard super smooth. Remove from heat and stir in the coconut, butter, vanilla, and coconut extract. If you've strained the mixture, add the ingredients to the bowl with the strained custard and stir to combine.
Pour the warm filling into the cooled pie crust. Cover tightly with plastic wrap putting the plastic wrap directly on the surface of the pudding to prevent a skin from forming. Refrigerate for at least 3 hours or overnight until chilled and completely set. The pie can be made and refrigerated for up to 1 day before topping with whipped cream and serving.
Make the whipped cream using a hand mixer or a stand mixer fitted with a whisk attachment, whip the heavy cream, sugar, and vanilla extract on medium-high speed until medium peaks form, about 3-4 minutes.
Dollop the whipped cream on top of the pie and spread to the edges of the custard leaving the crust exposed. Garnish with the unsweetened coconut. Chill the pie for a couple of hours or serve it immediately, your choice.Cover leftovers and store in the refrigerator for up to 5 days. I've never had it last that long, but you can keep it that long!!! Enjoy every bite.