In a saucepan, combine the sugar and water. Cook over medium heat, stirring constantly until the sugar dissolves and turns into a golden-brown caramel.
Immediately pour the caramel into the bottom of a 9-inch (23 cm) round baking dish or bundt pan, tilting the dish to coat the bottom evenly. Set aside to cool and harden.
In a large bowl, whisk together the sweetened condensed milk, evaporated milk, whole milk, eggs, and vanilla extract until smooth and well combined.
Pour the custard mixture over the hardened caramel in the baking dish.
Preheat your oven to 350°F (175°C).
Place the baking dish in a larger baking pan. Fill the larger pan with hot water until it reaches halfway up the sides of the baking dish (this is a water bath).
Bake in the preheated oven for about 50-60 minutes, or until the custard is set and a toothpick inserted into the center comes out clean.
Remove the baking dish from the water bath and let it cool to room temperature.
Refrigerate for at least 4 hours, or overnight.
To serve, run a knife around the edges of the dish to loosen the budin. Invert it onto a serving plate so that the caramel is on top.
Enjoy your meal!