Preheat oven to 350°F (175°C).
In a saucepan over medium-low heat, melt sugar until golden. Carefully pour hot syrup into a round baking dish, tilting to coat the bottom evenly. Set aside.
In a large bowl, beat eggs. Stir in condensed milk, evaporated milk, and vanilla until smooth. Pour egg mixture into the baking dish over the caramelized sugar.
Place the baking dish in a larger baking pan. Fill the larger pan with hot water to a depth of 1 inch.
Bake in the preheated oven for 60 minutes, or until the center is set. Let cool, then refrigerate for at least 4 hours or overnight.
To serve, run a knife around the edges of the dish, place a plate on top, and invert to release the flan.