Preheat the oven to 375°F (190°C).

Combine sugar and water in a medium saucepan over medium-high heat. Bring to a boil without stirring to avoid crystallizing. Cook until it browns (7-10 minutes), then pour into a 10-inch flan mold, moving it to coat the bottom evenly.

Combine evaporated milk, condensed milk, egg yolks, and vanilla extract in a bowl. Mix gently to avoid foam; strain the mixture.

Pour the custard mixture into the caramel-coated mold.

Prepare a water bath by placing the mold inside a roasting pan. Add hot water until it reaches halfway up the mold. Cover the roasting pan with foil.

Bake for approximately 1 hour or until a knife inserted near the center comes out clean.

Remove from oven and allow it to cool for 1 hour, then refrigerate for at least 4 hours or overnight.