Make the caramel by adding the sugar and water to a saucepan over low heat. Do not stir.
Bring the mixture to a gentle boil. Swirl the pan occasionally as needed and cook until the caramel turns golden amber. Turn off the heat.
Immediately divide the caramel between two 6-inch (15 cm) round cake pans. Carefully swirl each pan to evenly coat the bottom. Set aside.Pro Tip: Use oven mitts when swirling the caramel in the cake pans, as the pans will get very hot. In a large bowl, crack the eggs. Add the condensed milk, evaporated milk, and vanilla extract.
Mix until smooth and well combined using a hand mixer. You can also use a blender or whisk by hand.
Strain the custard mixture twice for a smooth texture.Pro Tip: For a smoother quesillo without a ruffled texture, let the custard sit for 10–15 minutes. Pour into the cake pans, then gently tap the pans to release any remaining bubbles. Divide the custard mixture evenly between the two prepared cake pans.
Cover the cake pans tightly with aluminum foil, crimping the foil around the edges to seal it.
Place the cake pans in a steamer and steam over low heat for 1 hour, or until the custards are set with a gentle jiggle in the center.
Remove the cake pans from the steamer and let the quesillo cool at room temperature for 2–3 hours. Cover and refrigerate for at least 6 hours, preferably overnight.
When ready to serve, place the bottom of the cake pans in a warm water bath for 10–20 seconds to loosen the caramel.
Run a thin knife around the edges of the quesillo to loosen it from the pan.
Place a serving plate over the cake pan. Carefully flip the pan over and lift it away. Slice each quesillo into 8 pieces and serve.