In a small saucepan, combine ½ cup sugar and 3 tablespoons water over medium heat. Stir until the sugar dissolves.

Stop stirring and let the mixture simmer for 5-7 minutes, swirling the pan occasionally, until it reaches a deep amber color.

Immediately pour the caramel into a 6-inch cake pan or six individual ramekins, tilting to coat the bottom evenly. Set aside to harden.

Preheat oven to 325°F (160°C).

Heat 2 cups of whole milk in a saucepan over medium heat until hot but not boiling.

In a separate bowl, whisk together 3 large eggs, 1 egg yolk, and ½ cup of sugar.

Slowly pour the hot milk into the egg mixture while whisking constantly to temper the eggs.

Stir in 1 teaspoon of vanilla extract and a pinch of salt.

Strain the custard through a fine-mesh sieve for a smooth texture.

Pour the custard mixture over the hardened caramel in the pan or ramekins.

Place the pan/ramekins into a larger baking dish and create a water bath by pouring hot water into the larger dish until it reaches halfway up the sides.

Bake for 40-45 minutes, until the edges are set and the center has a slight jiggle.

Remove from the oven, take the custard pan out of the water bath, and let it cool completely on a wire rack.

Cover the cooled custard with plastic wrap and refrigerate for at least 3 hours, or until firm.

To serve, run a thin knife around the edge of the custard. Place a serving plate on top and quickly invert the pan to release the pudding.