Preheat your oven to 400°F (200°C). Place the chilled pie crust into a 9-inch pie plate. Crimp the edges decoratively.

Line the pie crust with parchment paper or foil, then fill with pie weights, dried beans, or rice. Blind bake for 15 minutes.

Carefully remove the weights and parchment/foil. Prick the bottom of the crust with a fork several times. Return to the oven and bake for another 5-10 minutes, or until lightly golden. Remove from oven and let cool completely on a wire rack. Reduce oven temperature to 350°F (175°C).

In a large mixing bowl, whisk together the large eggs, egg yolks, granulated sugar, and cornstarch until smooth and pale.

In a medium saucepan, combine the whole milk and full-fat coconut milk. Heat over medium heat, stirring occasionally, until the mixture just begins to simmer and steam. Do not boil.

Slowly pour about half of the hot milk mixture into the egg mixture, whisking constantly to temper the eggs. This prevents the eggs from scrambling. Once combined, pour the tempered egg mixture back into the saucepan with the remaining hot milk.

Return the saucepan to medium-low heat. Cook, whisking continuously, for 5-8 minutes, or until the custard thickens significantly and comes to a gentle boil, with bubbles appearing and bursting on the surface. (Optional: For an extra smooth custard, strain it through a fine-mesh sieve at this point).

Remove the saucepan from the heat. Stir in the unsalted butter and vanilla extract until the butter is completely melted and incorporated. Fold in the 1 1/2 cups of shredded sweetened coconut.

Pour the warm coconut custard filling into the cooled, blind-baked pie crust. Gently spread to an even layer.

Bake in the preheated 350°F (175°C) oven for 30-35 minutes, or until the edges are set and the center of the pie jiggles only slightly when gently shaken. Over-baking can make the custard rubbery.

Remove the pie from the oven and let it cool completely on a wire rack for at least 2 hours before chilling.

Once cooled, cover the pie loosely with plastic wrap and refrigerate for at least 4 hours, or preferably overnight, to allow the custard to fully set.

Just before serving, toast the remaining 1/2 cup shredded sweetened coconut: Spread it in a single layer on a dry baking sheet or skillet. Cook over medium-low heat, stirring frequently, until golden brown (about 3-5 minutes). Watch carefully as it can burn quickly. Let cool.

Slice the chilled coconut custard pie and sprinkle generously with the toasted coconut before serving.