Preheat your oven to 400° F.

In a large bowl, whisk together the eggs, sugar, salt, and vanilla extract. Pour in the scalded milk and mix until everything is well combined. Let the milk cool if it was scalded.

Use a pastry brush to coat the inside of the pie shell with the beaten egg white. Pour the custard mixture into the pie shell. Lightly sprinkle the nutmeg on top using a fine-mesh strainer.

Bake in the preheated oven for about 40 to 50 minutes. The edges should be set and the center should still jiggle slightly. Let the pie cool on a rack, then refrigerate before serving.