Preheat oven to 180°C and grease a cake tin or line with a baking sheet.
Mash the bananas.
Beat the eggs with the sugar, crème fraiche, oil and vanilla until smooth.
In another bowl, mix flour, baking soda and baking powder.
Add the flour mixture to the wet mixture and fold the two together. You could use a whisk or electric mixer, but down overmix.
Fold in the mashed banana.
Pour the batter into the prepared cake tin and bake for ca. 60 minutes in the middle of the oven.