On a lightly floured surface, roll the pie crust into a 13-inch circle. (Roll from the center to the edge, turning and flouring the dough so it doesn't stick to the board.)
Roll the dough onto your rolling pin. Unroll the dough into the pie pan without stretching. Press the dough into the pie pan and trim the excess dough, leaving a 1-inch overhang around the pan. Fold the edge under and crimp with either your fingers or the tines of a fork. Refrigerate the crust for 1 hour, or freeze for 30 minutes.
While the crust chills, preheat the oven to 425°F.
Place a round of parchment paper inside of the crust, and press a piece of aluminum foil onto the paper, pushing it against the sides of the crust. (This will keep your pie crust propped up during baking.) Fill the foil with pie weights or dry beans. Bake for 15 to 25 minutes until the edges are golden brown.
Meanwhile, in a small bowl, whisk together the egg and heavy cream.
Carefully remove the paper, foil and pie weights. Prick the crust 10 to 12 times all over the bottom with the tines of a fork and brush with the egg wash. Tent just the edges of the crust with foil.
Bake for another 10 to 15 minutes, or until the crust is golden all over. (I tent my crust during this step which just means that you're covering the crust's edge in foil so it doesn't burn while the center is crisping up.)
For the Filling:
In a medium, heat-proof bowl, whisk together the two eggs and two egg yolks, then set aside.
In a small pot, combine the half and half or milk and coconut milk. Place over medium heat. Stir occasionally, removing from heat once the coconut solids are completely dissolved and the mixture is warm, 3 to 5 minutes.
In a medium pot, combine the sugar, cornstarch, and salt. Whisk to combine, then pour in the milk mixture and whisk again to distribute all the dry ingredients. You don't want clumps!
Place over medium heat and cook, whisking constantly, until it starts to bubble and thicken, about 5 minutes. The mixture will coat the back of a spoon, and you'll see a noticeable difference in the consistency. Remove from the heat.
Time to temper the eggs! Slowly drizzle in 1 cup of the hot milk mixture to the eggs while whisking vigorously. Slowly pour the tempered egg mixture back into the pot, while whisking, and return to medium heat. Cook, gently whisking frequently, until thickened and the whisk leaves a trace when swooped through it. This should take 2 to 3 minutes, but may take longer depending on your stove. Remove from the heat.
Add the butter and stir until the butter is all melted. Mix in the toasted coconut and allow to cool for about 10 minutes. Then pour the filling into the baked pie shell. Smooth it into an even layer, cover, and refrigerate for at least 6 hours, or for best results, overnight.
For the Whipped Cream Topping:
When you’re ready to serve, in the bowl of a stand mixer with the whisk attachment, combine the heavy cream, powdered sugar, and vanilla. Beat on high speed until soft peaks form, about 2 minutes.
Dollop the whipped cream over top of the pie before serving. For a final touch, you can sprinkle with more toasted coconut.
Video
Notes
To toast the coconut: Spread the shredded coconut in an even layer on a baking sheet. Bake at 350°F, stirring every 2 to 3 minutes or when the coconut on the edges of the tray starts to toast, until evenly golden brown. This should take 5 to 8 minutes. You can find more details in my post about how to toast coconut.
Instead of spreading the whipped cream, you can pipe it with a tip of your choice. Check out my post on making your own whipped cream if you want more guidance on making it.
For a pretty garnish, you can use large flakes of coconut. I don't like them for the filling as they are too big and chewy, but they make a lovely finish to the pie.