Preheat your oven to 350°F (175°C).
In a medium saucepan over medium heat, melt the sugar until golden. Quickly pour into a 9-inch round baking dish, swirling to coat the bottom evenly.
In a large bowl, beat the cream cheese until smooth. Add eggs one at a time, mixing well.
Blend in sweetened condensed milk, evaporated milk, and vanilla extract until smooth and creamy.
Pour the cream cheese mixture over the caramel in the baking dish.
Place the dish in a larger pan filled with about 1 inch of hot water (water bath).
Bake for about 50–60 minutes, or until the center is set and a knife inserted comes out clean.
Cool completely, then refrigerate for at least 4 hours or overnight.
To serve, run a knife around the edges and invert onto a serving plate.