Prepare the Caramel
In a medium saucepan over medium heat, melt the granulated sugar until it turns golden brown and smooth. Stir gently to avoid clumps.
Immediately pour the caramel into a 9-inch round baking dish, tilting it to coat the bottom evenly. Set aside to let the caramel harden.
Make the Custard
In a mixing bowl, whisk the eggs until well blended.
Add the sweetened condensed milk, evaporated milk, and vanilla extract. Mix until smooth.
For an extra silky texture, strain the custard through a fine-mesh strainer into a clean bowl.
Combine and Bake
Pour the custard mixture over the hardened caramel in the baking dish.
Place the baking dish inside a large roasting pan. Pour hot water into the roasting pan until it reaches halfway up the sides of the flan dish (this creates a water bath).
Cover the flan with aluminum foil and bake at 350°F (175°C) for 50-60 minutes, or until the flan is set but slightly jiggly in the center.
Cool and Chill
Remove the flan from the oven and let it cool to room temperature.
Refrigerate for at least 4 hours or overnight for the best texture.
Unmold and Serve
Run a knife around the edges of the flan to loosen it.
Place a serving plate over the baking dish and carefully invert the flan onto the plate. The caramel will flow over the top as a sauce.