Preheat your oven to 350°F (175°C).

In a small saucepan, combine granulated sugar and water over medium heat. Stir until the sugar dissolves and cook until it turns a light amber color to make the caramel.

Quickly pour the caramel into a round baking dish, tilting to coat the bottom evenly. Set aside to cool and harden.

In a blender, mix together the sweetened condensed milk, whole milk, eggs, dark rum, and vanilla extract until smooth.

Pour the milk mixture over the hardened caramel in the baking dish.

Place the baking dish in a larger pan and fill the larger pan with hot water halfway up the sides of the baking dish to create a water bath.

Bake in the preheated oven for 75 minutes or until the center is just set.

Remove the quesillo from the oven and let it cool to room temperature. Then, refrigerate for at least 4 hours or overnight.

To serve, run a knife around the edges of the dish and invert onto a serving plate. The caramel sauce will flow over the quesillo.