Preheat the oven to 350°F (175°C).
Make the caramel: in a heavy saucepan, melt the Granulated Sugar over medium heat, swirling occasionally, until it turns a deep amber color. Immediately and carefully pour the caramel into a round baking dish or individual ramekins, tilting to coat the bottom evenly; set aside to harden.
Prepare the custard: soften and smooth the Cream Cheese in a large bowl or in a blender until there are no lumps.
Add the Sweetened Condensed Milk and Evaporated Milk to the cream cheese and blend or whisk until fully combined and silky.
Temper in the Eggs by whisking them lightly, then mixing them into the dairy mixture until uniform; stir in the Vanilla Extract. Avoid whipping in too much air to keep the custard smooth.
For an ultra-silky texture, strain the custard through a fine-mesh sieve into a pouring jug to remove any remaining bits.
Pour the custard gently over the set caramel in the prepared dish or ramekins.
Place the filled dish(es) in a larger baking pan and pour hot water into the outer pan to come about halfway up the sides of the flan dish (a bain-marie). Cover the flan loosely with foil.
Bake for 45–60 minutes, or until the center is mostly set but still has a slight jiggle (a knife inserted near the center should come out mostly clean). Baking time will vary with dish size.
Remove the flan from the water bath and let cool to room temperature, then refrigerate for at least 4 hours or overnight to fully set and chill.
To unmold, run a thin knife around the edge of the flan to loosen, invert onto a serving plate, and let the caramel sauce drizzle over the top. Serve chilled.
