Preheat your oven to 350°F (175°C) and boil a kettle of water for the water bath. Place a 9-inch round baking dish inside a larger, high-sided roasting pan.

In a medium saucepan, combine the granulated sugar and water over medium heat. Stir gently just until the sugar dissolves, then stop stirring and let it boil until it turns a deep amber color, about 8 to 10 minutes.

Immediately pour the hot caramel into the 9-inch baking dish, carefully swirling the dish to coat the bottom evenly. Set the dish aside to cool and allow the caramel to harden for at least 10 minutes.

In a large bowl or blender, combine the sweetened condensed milk, evaporated milk, whole eggs, egg yolks, vanilla extract, and salt. Whisk or blend until the mixture is completely smooth and well combined.

Pour the custard mixture through a fine-mesh sieve directly over the hardened caramel in the baking dish to ensure a perfectly silky, lump-free texture.

Carefully pour the boiling water into the larger roasting pan until it reaches halfway up the sides of the 9-inch dish, creating a water bath (bain-marie) that will gently cook the custard.

Bake for 45 to 55 minutes, or until the edges are beautifully set but the center still has a slight jiggle when gently shaken. Carefully remove the baking dish from the water bath and let it cool completely on a wire rack.

Cover the cooled flan tightly with plastic wrap and refrigerate for at least 4 hours, or preferably overnight. To serve, run a sharp knife around the edges, place a large serving plate upside down over the dish, and quickly invert to release the flan and its gorgeous caramel sauce.