-
In a large saucepan, mix together sugar, cornstarch, and salt.
-
Stir in 1 cup of the coconut milk until smooth.
-
Over medium heat, cook until mixture begins to thicken, whisking constantly.
-
When mixture begins to thicken, add in remaining two cups of coconut milk in a slow stream, whisking constantly.
-
Continue to stir until mixture continues to thicken and begins to bubble. Boil 1 minute. Remove from heat while completing the next step.
-
Taking a large ladle, put between 1 1/2 to 2 cups of the hot milk mixture into a liquid measuring cup for easy pouring.
-
Slowly pour hot milk mixture into beaten egg yolks, whisking rapidly (with a whisk or a fork) to prevent lumping.
-
Return saucepan to heat and slowly pour yolk mixture back into remaining milk mixture, continuing to whisk rapidly.
-
Reduce heat to low. Cook for about two more minutes or until mixture is very thick, stirring constantly.
-
Remove saucepan from heat. Stir in butter and vanilla extract until butter has melted completely.
-
Set aside filling to cool slightly, stirring occasionally, to prevent a skin.
-
Using a fine mesh sieve, strain pudding into prepared pie shell and spread evenly.
-
Place plastic wrap directly on surface of filling and refrigerate pie until filling is set (about 3 hours).