Preheat the oven to 350°F (175°C) and place the pie crust into a glass or ceramic dish.
Whisk together the eggs, sugar, salt, vanilla, and milk gently until smooth without creating bubbles.
Strain the custard mixture through a mesh sieve into a bowl to remove any egg bits for a silky texture.
Pour the strained custard into the pie crust and sprinkle lightly with nutmeg for classic old-fashioned flavor.
Bake until the edges are set and the center has a soft wobble, then cool completely to allow the custard to firm.