In a large mixing bowl, whisk together the sugar, cornstarch, and salt.
Add the eggs and rum (or other liquor) and whisk until smooth. Set aside.
In a medium pot over medium heat, bring the milk, cream, and nutmeg to just under a boil.
Once the mixture is hot and steaming, transfer it to a heatproof measuring cup. Very slowly pour it into the bowl from step one while whisking constantly and vigorously. This gradual process tempers the eggs and ensures a smooth, creamy pudding.
When all of the liquid 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 the pudding reaches a boil, whisk vigorously for 30 to 60 seconds.
Immediately strain the pudding through a fine-mesh sieve into a clean mixing bowl to remove any lumps or bits of cooked egg.
Whisk in the butter and vanilla extract until smooth.
Pour the warm pudding directly into your prepared gingersnap pie crust and spread it evenly.
Press a piece of plastic wrap directly against the surface to prevent a skin from forming.
Chill the pie for at least 3 hours, or until the filling is fully set and cool to the touch.