Preheat oven to 350ºF.

Caramel Sauce:
Melt 1 cup of the sugar in a small saucepan over a medium heat, swirling occasionally, for 8 to 10 minutes. When the sugar turns golden brown, add 1/2 cup of the water, and using a long-handled spoon slowly stir in the water. Cook the caramel sauce for 2 to 3 minutes, stirring constantly. Remove the pan from the heat. Into each of 12 custard cups or ramekins, pour enough hot caramel to coat the bottom. Put the custard cups in a 2-inch deep baking pan, and fill the pan with very hot water until it comes halfway up the sides of the cups. Set the cups aside while making the custard.

Custard:
Heat the milk in a large pan over medium high heat until it simmers, watching carefully. Remove from the heat. In a separate bowl, combine the remaining 1 1/2 cups sugar, the eggs, and the vanilla extract. Whisk until smooth. Slowly add the milk to the eggs to temper them and avoid scrambling the eggs. Once all of the milk has been incorporated, pour the custard through a fine mesh strainer.

Fill each of the caramel coated cups with liquid custard. Cover the pan with foil, and create a seal at the edges. Bake the custards in a water bath for 30 minutes.

Remove the foil, and Bake for an additional 30 to 40 minutes. To check for doneness, touch the top of the custard. It should have a light, springy texture that does not stick to your finger.

Remove the custards from the water bath, let them cool to room temperature, and refrigerate until chilled.

Separate the custards from the sides of the cups using a small paring knife. Invert the cups onto small dessert plates or bowls. Remove the cups to allow the rich caramel sauce to run down the sides of the custards.