In a heavy-bottomed saucepan, combine the 1 cup of sugar and water. Gently swirl the pan over medium heat until the sugar dissolves. Once it starts boiling, stop swirling! Let it bubble away until it turns a beautiful golden-amber color. This takes about 8-10 minutes. Please be careful, melted sugar is extremely hot. Immediately pour the hot caramel into a 8-inch round baking dish or 6 ramekins, tilting to coat the bottom evenly. Set aside to harden.

While the caramel sets, gently warm the milk in a saucepan or the microwave until it's just steaming. You don't want it boiling, just hot to the touch.

In a large bowl, whisk the whole eggs, egg yolks, and the remaining 1/2 cup of sugar together until the mixture is pale yellow and slightly fluffy. Whisk in the vanilla extract and pinch of salt.

Slowly pour the warm milk into the egg mixture, whisking constantly. We do this slowly to prevent the hot milk from scrambling the eggs. You should have a smooth, thin custard.

Place your caramel-coated dish (or ramekins) in a large roasting pan. Strain the custard mixture through a fine-mesh sieve into the dish—this catches any bits of egg for the silkiest texture. Pour hot water into the roasting pan until it comes about halfway up the sides of your pudding dish. This "bain-marie" ensures gentle, even cooking.

Carefully transfer the pan to a preheated oven at 325°F (160°C). Bake for 40-50 minutes, or until the custard is set around the edges but still has a slight jiggle in the center. Remove from the oven and the water bath. Let it cool completely on a wire rack before covering and refrigerating for at least 2 hours, but preferably overnight.