In a large mixing bowl, whisk together the sugar, cornstarch, and salt.
Add the egg yolks and whisk together with the dries from step 1 until the egg yolks are broken up. You do not need to fully mix everything together. Set aside.
In a medium pot over medium heat, bring the milk to just under a boil.
Once the milk is hot and steaming, transfer the milk to a heatproof measuring cup. Very slowly pour it into the bowl from step two while whisking constantly and vigorously.
When all of the milk has been added, pour the mixture back into the pot. Place it over low heat and whisk continuously until the pudding thickens and just begins to bubble.
As soon as it reaches a boil, whisk vigorously for 30 to 60 seconds.
Immediately strain the vanilla pudding through a fine-mesh sieve into a clean mixing bowl.
Whisk in the butter and vanilla extract until smooth.
Pour the pudding into your prepared graham cracker crust.
Press a piece of plastic wrap directly against the surface to prevent a skin from forming.
Chill the pie in your refrigerator for at least 3 hours so the pudding can fully set.