Preheat your oven to 325 degrees Fahrenheit.

Lightly butter or oil a 9-inch round baking dish to prevent sticking.

Crack all four eggs into a medium mixing bowl and add the sugar. Whisk vigorously for about two minutes until pale yellow and slightly thick.

Pour in the milk slowly while whisking continuously. Add vanilla extract and salt, whisking until fully blended. Strain mixture through a fine-mesh sieve if lumps appear.

Transfer the custard mixture into the prepared baking dish. Skim any excess foam from the surface with a spoon.

Place the baking dish into a larger roasting pan. Pour hot water into the roasting pan until it reaches halfway up the sides of the baking dish to create a water bath.

Carefully transfer the water bath to the oven and bake for 35 to 40 minutes. The pudding is set when the edges are firm but the center has a slight jiggle about a quarter inch in diameter; the center temperature should be 170 to 175 degrees Fahrenheit.

Remove the baking dish from the water bath and let cool to room temperature for about 30 minutes. Refrigerate for at least two hours before serving to allow flavors to develop and pudding to firm up.

Serve chilled or gently warm in the microwave for 20 to 30 seconds if preferred. Optionally, sprinkle with a pinch of nutmeg before serving.