In a medium bowl, combine the flour, 1 teaspoon sugar, and 1/2 teaspoon salt.
Cut in the 1/2 cup cold cubed butter with a pastry cutter or fork until pea-sized chunks remain.
Stir in 3 to 4 tablespoons cold water gradually until the dough can be pressed together.
Form the dough into a disk, wrap in plastic wrap, and refrigerate at least 2 hours (or freeze 30 minutes) until chilled.
Preheat the oven to 425°F (220°C). Roll out the chilled dough to fit a 9-inch pie plate.
Press the dough into the pie plate and up the sides, trim and crimp the edges as desired, then dock the bottom and sides with a fork (or use pie weights).
Bake the crust 10–15 minutes until light golden brown, then set aside to cool while you prepare the filling.
In a large saucepan, whisk together 2 cups coconut milk, 1/2 cup granulated sugar, 3 large eggs, and 3 tablespoons cornstarch until smooth.
Cook over medium heat, whisking frequently, and add the 1 teaspoon coconut extract and 1 teaspoon vanilla extract; continue stirring until the mixture becomes very thick, about 10–15 minutes.
Pour the hot filling into the cooled pie crust; press a piece of parchment onto the surface, then refrigerate until well chilled, at least several hours or overnight.
Top the chilled pie with whipped cream and sprinkle with toasted coconut before serving.