Preheat the oven to 350°F (180°C).
Beat the eggs, sugar and vanilla until well combined. Add the oil and mix.
Add the flour and baking powder, then the milk, and beat until just blended.
Gently pour the batter over the creme mixture.
Set the cake pan inside a larger baking dish. Pour boiling water into the larger dish until it reaches halfway up the sides of the cake pan.
Bake in the water bath for 1 hour, or until the center is set and a toothpick in the cake layer comes out clean.
Cool at room temperature for 1 hour, then refrigerate at least 4 hours, preferably overnight.
To serve, set the pan in hot water for 1 minute to loosen the caramel. Run a knife around the edge, place a serving plate on top, and flip.
Enjoy serving it, and even more, eating it!