Preheat the oven to 350 and line two or three baking sheets with baking parchment.
Put the eggs and brown sugar in a large bowl and whisk together until well blended. Stir in the vanilla extract. Add the oil and creme fraice and stir in well. Add the flour and mix well. (The mixture will be quite runny at this stage.) Cover with plastic wrap and chill in the refrigerator for about 30 minutes.
Put the frosted cornflakes in a large bowl. Remove the cookie dough from the refrigerator and stir in the bananas. Using a tablespoon, drop heaps into the flakes. Lightly toss so each cookie is well coated, then remove and place on the prepared baking sheets. Flatten very slightly with your fingertips.
Bake for 15-20 minutes, or until risen and golden brown and crispy. Transfer the cookies to a wire rack and dredge with sifted confectioners' sugar. Serve while still warm.