1. Place the whole can of coconut milk into a large measuring cup. It will measure a little over 1 1/2 cups. Pour the Half and Half into the same measuring cup on top of the coconut milk until you reach the 3 cup measurement. Stir to combine the half and half and coconut milk.
2. Place the coconut/half and half mixture into a medium size heavy metal saucepan. Place the 4 beaten egg yolks ,3/4 cup of sugar , salt and the 1/3 cup of corn starch into the pan as well. Whisk to combine. Turn your burner on low. Place the pan on low heat and slowly whisk . Keep whisking, this is the part that needs just a little patience. It can take up to 15 minutes for the ingredients to thicken. DO NOT turn the heat up to speed up the process. As you whisk you will start to feel a slight resistance to the whisk as you make your way around the pot. The pudding is starting to thicken. Don't walk away from the pot, when it starts to thicken it will happen all at once.
3. Keep whisking until the pudding starts to boil, it will release thick bubbles that will come to the top like a little volcano. It has to reach this stage for it to set up properly. Once it starts to boil, whisk a little faster for a minute. Take the pudding off the heat and add the vanilla, butter and coconut. Mix to combine.
4. Pour the pudding into the pie crust while it's hot. It's going to fill that pie crust to the brim! Place a piece of plastic wrap on top of the pudding, pressing down on the surface of the pudding slightly so the plastic wrap sticks to it to prevent a film from forming on the pudding when it cools. Refrigerate pie for about 4 hours. Top with homemade whipping cream or Cool Whip.