Preheat the oven to 350°F (175°C).
In a small saucepan over medium heat, melt sugar until golden. Carefully pour hot syrup into a round baking dish, turning the dish to evenly coat the bottom.
In a large bowl, whisk together sweetened condensed milk, evaporated milk, eggs, and vanilla until smooth.
Pour egg mixture over the caramel layer in the baking dish.
Place the baking dish in a larger pan, and pour boiling water into the larger pan to a depth of about 1 inch.
Bake in the preheated oven for 60 minutes, or until the center is set.
Remove from oven and let cool before refrigerating for at least 4 hours. To serve, invert onto a plate.