Combine the sugar and water in a small saucepan over medium heat. Cook without stirring, swirling the pan occasionally, until it reaches a golden amber color.

Immediately pour the caramel into a ramekin, tilting it to coat the bottom evenly. Let it cool and harden completely.

Warm the milk in a small saucepan over medium-low heat until tiny bubbles form at the edges (do not boil). Turn off the heat source, then add the sweetened condensed milk, and vanilla extract. Whisk gently until fully combined. Remove from heat and let cool slightly to prevent curdling during tempering.

In a mixing bowl, whisk together the whole egg and egg yolk , after adding a small pinch of salt. Gradually temper the eggs by slowly adding the warm flavored milk in small increments while whisking constantly. This ensures a smooth custard without cooking the eggs.

Strain the mixture through a fine-mesh sieve to ensure a smooth custard.

Pour the mixture into the ramekin over the hardened caramel. Place the ramekin in a deep baking dish. Fill the dish with hot water until it reaches halfway up the ramekin (creating a water bath). Cover the entire baking dish with aluminum foil before placing it in the oven to retain moisture and ensure even cooking. Bake at 140°C (285°F) for 55-60 minutes, or until the flan is just set with a slight jiggle in the center.

Remove the ramekin from the water bath and allow it to cool to room temperature. Cover and refrigerate for at least 2 hours (or overnight for best results).

To serve, run a knife around the edge of the flan and invert it onto a plate. Let the caramel sauce flow over the top.