Preheat your oven to 350°F (175°C)
In a heavy-bottomed saucepan, melt the sugar over medium heat, stirring constantly until it turns into a golden amber caramel. Pour the caramel into a flan mold, tilting to coat the bottom evenly
In a mixing bowl, whisk together the evaporated milk, condensed milk, eggs, vanilla extract, and whole milk until smooth.
Stir in the shredded cheese.
Pour the mixture into the caramel-coated mold
Place the mold in a larger baking pan and add hot water to the pan, creating a water bath that comes halfway up the sides of the mold
Bake for 1 hour, or until the quesillo is set but still slightly jiggly in the center
Remove from the oven and let cool completely
Refrigerate for at least 4 hours, or preferably overnight
To serve, run a knife around the edge of the mold and invert onto a serving plate. Let the caramel drizzle over the quesillo
Slice and serve cold