Beat eggs with sugar, salt, and vanilla in a bowl. Slowly whisk warm milk into the egg mixture. Pour through a strainer into a 1 1/2-quart round baking dish. Sprinkle nutmeg over the mixture. Place the baking dish into a larger pan. Pour about 1 inch of water into the larger pan.
Bake in the preheated oven until a knife inserted into the center comes out clean, 55 to 60 minutes. Cool to room temperature. Chill to serve.
