Whisk 1/4 cup of the milk, eggs, corn starch, salt and sugar in a bowl.
In a heavy saucepan, heat remaining 2 3/4 cups of milk until hot but not boiling.
Slowly pour 1/2 the hot milk into the egg mixture to temper. Then add all the tempered egg mixture back to the hot milk. Whisk constantly on medium low heat for up to 2 minutes until mixture thickens into a custard. Remove from heat . Let bubbles form in the custard, but do not allow the custard to come to a full boil.
Remove the saucepan from the heat and stir in coconut and vanilla.
Pour in baked crust and chill at least 3 hours or up to 24 hours before serving.