Beat the eggs and sugar doe 2 minutes, until the sugar is dissolved. Add the vanilla and milk, whisk to combine. Set aside.
In a bowl sift together the flour, baking powder and cocoa powder. Set aside.
Beat the egg and sugar together for 2 minutes. Add the vanilla and oil. Beat to combine. Add the milk and yogurt and mix to incorporate. Add the dry ingredients and beat until just combined.
Heat caramel in a saucepan over medium heat, stirring constantly with a rubber spatula. Let it caramelize until it gets for an amber color (about 5-7 minutes), depending on the pan and stove you use.
Spray a bundt pan with cooking spray. Add the caramel on the bottom.
Preheat oven to 350F.
Prepare a larger pan for the double boiler.
Pour the custard mixture over the caramel. Add the chocolate cake on top, try to pour it evenly. It will sink, but will rise while baking.
Place the bundt pan in the larger pan. Pour cold water, filling the outer pan about 1-inch below the top.
Bake for 60-70 minutes,(toothpick inserted into the top layer should come out clean) then let it cool inside the oven for 30 minutes.
Refrigerate for 2 hours.
When ready to serve, invert the dessert onto a platter.
Slice and serve.