Pie crust:

In a medium bowl, stir together the flour, sugar, and salt.
Cut in butter with a pastry cutter or fork until you see pea-sized chunks of butter remaining.
Gradually add in cold water, stirring each time until you can press it together.
Form it into a disk, wrap in plastic wrap, and refrigerate for at least 2 hours, or freeze for 30 minutes until chilled.
Preheat oven to 425°F (220°C).
Roll out to fit a 9″ pie plate.
Press into the pie plate and up the sides. Try to get as high up the sides as you can as the pie crust may shrink when it bakes. Trim the edges and crimp or leave as desired. Poke the bottom and the sides with a fork all over to help prevent puffing (or use pie weights if you have them).
Bake for 10-15 minutes until light golden brown. Set aside to cool while you make the filling.
Filling:

In a medium saucepan, combine coconut milk, sugar, and corn starch. Cook over medium heat, stirring constantly until thickened.
In a separate bowl, beat the eggs, then slowly whisk in a small amount of the hot coconut milk mixture to temper the eggs.
Gradually add the tempered egg mixture back into the saucepan, stirring constantly.
Continue cooking until the mixture is thick and bubbly.
Remove from heat and stir in coconut extract and vanilla extract.
Pour the filling into the cooled pie crust.
Refrigerate for at least 2 hours or until set.