1. Prepare the caramel by melting sugar in a pan until it turns amber-colored.
2. Quickly pour the caramel into ramekins or a large mold, coating the bottom evenly.
3. In a bowl, whisk eggs with sugar until well combined.
4. Heat milk with vanilla until warm, then slowly add it to the egg mixture while stirring continuously.
5. Strain the custard mixture to remove any lumps for a smooth texture.
6. Pour the custard mixture over the hardened caramel in the ramekins or mold.
7. Place the ramekins or mold in a baking dish and add hot water to create a water bath.
8. Bake in a preheated oven at a moderate temperature until the custard is set but slightly jiggly in the center.
9. Remove from the oven and let it cool to room temperature.
10. Refrigerate for several hours or overnight to allow the flan to firm up.
11. Run a knife around the edges of the ramekin or mold to loosen the flan.
12. Invert onto a plate so the caramel sauce flows over the custard.
13. Serve chilled and enjoy your creamy, silky Flan Creme Caramel.