Preheat oven to 350°F and place the unbaked pie crust in a 9-inch pie pan.
In a large bowl, whisk together eggs, sugar, and salt until well combined and slightly frothy.
Heat milk in a saucepan until warm but not boiling, then slowly whisk the warm milk into the egg mixture to temper the eggs.
Stir in vanilla extract, then carefully pour the custard mixture into the unbaked pie shell.
Sprinkle nutmeg evenly over the top of the custard.
Bake for 40-45 minutes, until the edges are set but the center still jiggles slightly when gently shaken.
Cool completely on a wire rack, then refrigerate for at least 2 hours before serving.