Position a rack in the lower third of the oven and preheat it to 325°F (163°C). Set an ungreased 8 by 2-inch round metal cake pan inside a large roasting pan to confirm it sits flat with room for water around it, then remove the cake pan. Bring a kettle of water to a simmer for the water bath. Place a dry heatproof towel beside the stove so the caramel-coated pan has a safe landing spot.
Combine the granulated sugar and water in a medium heavy-bottomed saucepan. Stir gently only until every grain is moistened, then cook over medium heat without further stirring for 8 to 10 minutes. Swirl the pan occasionally as the syrup colors, removing it from the heat when it reaches an even deep amber and smells toasted, not burned. Carefully pour the hot caramel into the cake pan and tilt with oven mitts to coat the bottom. Set aside until hardened.
Place the eggs, egg yolks, vanilla, and salt in a large bowl and whisk slowly until the whites and yolks are fully blended without becoming foamy. In a separate heatproof jug, whisk the dulce de leche with about one-third of the evaporated milk until smooth. Add the remaining evaporated milk and whole milk, then pour this mixture gradually into the eggs while whisking gently. Stop as soon as the custard is uniform; vigorous mixing traps air that can create holes.
Set a fine-mesh sieve over a clean jug or bowl with a pouring spout and strain the custard, using a flexible spatula to encourage it through without pressing any firm egg fragments. Skim visible foam from the surface with a spoon. Place the caramel-lined cake pan back inside the roasting pan, then slowly pour in the custard. If bubbles remain, touch them with the corner of a paper towel rather than stirring. Loosely tent the pan with aluminum foil.
Place the roasting pan on the extended oven rack, then carefully pour the simmering water around the cake pan until it reaches halfway up the sides. Slide the rack in without splashing water into the custard. Bake for 55 to 65 minutes, removing the foil for the final 10 minutes to check the surface. The edges should be set, while a 2-inch area in the center trembles as one unit. An instant-read thermometer inserted near the center should register about 175°F.
Using oven mitts, lift the flan pan straight out of the water bath and place it on a wire rack. Remove the foil and let the custard cool for 60 to 90 minutes, until the pan no longer feels warm, keeping total room-temperature time under 2 hours. Cover the pan without touching the surface and refrigerate for at least 6 hours, preferably overnight. This rest firms the custard and allows hardened caramel to dissolve into a fluid sauce.
Remove the thoroughly chilled flan from the refrigerator. Run a thin paring knife once around the edge, keeping the blade against the pan so the custard stays smooth. Set the pan in warm water for 10 to 15 seconds to loosen the caramel, then dry the outside. Center a rimmed serving platter over the pan, hold both firmly, and invert in one confident motion. Pause for several seconds before lifting the pan so the custard and caramel release completely.