Preheat oven to 350°F (175°C).
In a medium saucepan over medium-low heat, melt sugar until golden. Carefully pour hot caramel into a round glass baking dish, turning the dish to evenly coat the bottom and sides. Set aside.
In a blender, combine sweetened condensed milk, evaporated milk, eggs, and vanilla. Blend on high until smooth. Pour mixture into the baking dish over the caramel.
Place the filled baking dish in a larger baking pan. Fill the larger pan with hot water to reach halfway up the sides of the baking dish.
Bake in preheated oven for 60 minutes. Let cool completely, then refrigerate for at least 4 hours before serving.
To serve, run a knife around the edges of the dish, invert onto a serving plate, and enjoy!