Set an 8-inch round metal cake pan or a large llanera nearby. Place a steaming rack in a large pot with a tight-fitting lid. Add water to come just below the rack, then bring it to a gentle simmer.

Make the caramel: add the sugar and water to a small, heavy saucepan over medium heat. Swirl the pan occasionally, but do not stir once the sugar begins to melt. Cook until the syrup is a deep amber color, about 6 to 8 minutes. Immediately and carefully pour the hot caramel into the cake pan. Tilt the pan to coat the bottom, then set it aside to harden.

In a large bowl, gently whisk the egg yolks just until combined. Add the sweetened condensed milk, evaporated milk, and vanilla. Whisk slowly until smooth, taking care not to create lots of bubbles.

Pour the custard through a fine-mesh strainer into the caramel-lined pan. Cover the pan tightly with foil.

Set the covered pan on the rack over gently simmering water. Wrap the pot lid with a clean kitchen towel to catch condensation, keeping the towel safely away from the burner. Cover and steam until the center is set but has a slight jiggle when the pan is moved, about 35 to 45 minutes. Add more hot water to the pot if needed during steaming.

Carefully remove the pan from the pot and let it cool at room temperature. Refrigerate until thoroughly chilled and firm, at least 4 hours or overnight.

To serve, run a thin knife around the edge of the cold flan. Place a rimmed serving plate over the pan, then quickly invert both together. Lift off the pan and slice the leche flan, spooning the caramel sauce over each serving.