Preheat oven to 325°F (160°C).
Start by making the caramel sauce: Place ½ cup of granulated sugar with 1 tablespoon of water in a saucepan over medium low heat. Stir continuously until the sugar melts and turns into a golden brown caramel, add the remain 2 tablespoon of water carfully. Then remove from heat.
Immediately pour it into the bottom of your flan mold or ramekins. Let it cool and harden while you prepare the custard.
Heat the milk on a medium heat.
In a medium bowl, add the 3 eggs, 1 egg yolk, the remain ½ cup of sugar and vanilla extract and beat them lightly with a whisk.
Add the hot milk to the beaten eggs and mix until well combined.
Strain the flan mixture in a measuring cup with a strainer.
Pour the mixture over the hardened caramel in the mold or ramekins.
Cover the mold or ramekins with aluminum foil.
Place the covered mold or ramekins in a larger baking dish. Fill the larger dish with hot water until it reaches about halfway up the sides of the mold or ramekins. This water bath helps ensure even cooking.
Carefully transfer the baking dish to the preheated oven and bake for 40-50 minutes. The custard should be set but still slightly jiggly in the center when gently shaken, or You can insert a toothpick in the middle of the flan and if it comes out clean then it is ready.
Remove from the oven and let it cool on a wire rack at room temperature.
Once cooled, refrigerate the flan for at least 2 hours or overnight to allow it to fully set and chill.
To serve, run a knife around the edges of the mold or ramekins to loosen the flan. Place a serving plate over the top and invert it to release the dessert. The caramel will flow over the custard, creating a delicious sauce.