Preheat oven to 350 degrees F. Thoroughly grease about 24 muffin cups.

In a large mixing bowl, beat together the egg and mayonnaise. Add the ripe bananas and beat until smooth. You can do this by hand or preferably, with a handheld electric mixer.

Beat in the sugar, brown sugar, vanilla, baking soda and salt. Stir in the flour.

Divide the batter between muffin cups (it should be about ⅔ of the way full) and bake for about 25 minutes or until muffins are set. Let cool slightly, then turn from pan. The muffins have flat tops, so I like to serve them upside down with a dab of cream cheese icing. To make as a loaf, bake in a 9x5 inch baking pan for 1 hour.