Preheat the 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 baking dish, turning the dish to evenly coat the bottom. Set aside.
In a blender, combine sweetened condensed milk, evaporated milk, eggs, cream cheese, and vanilla extract. Blend until smooth.
Pour the blended mixture over the caramel in the baking dish.
Place the baking dish in a larger pan and fill the larger pan with hot water to reach halfway up the sides of the baking dish.
Bake in the preheated oven for 60 minutes, or until the center is just set. Let cool, then refrigerate for at least 4 hours before serving.
To serve, run a knife around the edges of the baking dish and invert onto a serving plate.