Ok, so mayonnaise isn't something you would normally find in a cupcake recipe, but for whatever reason it works and makes really moist cupcakes.
I have made this recipe several times as I wanted a moist result as many recipes create a drier muffin. This was exceptionally popular with my family & friends and they keep well. My grandchildren love them. Have also added blueberries and today strawberries. - 16 Nov 2016
This one is A KEEPER! I have been searching for the perfect banana bread/muffin recipe for years, and I have finally found it. For those of you who may be thinking "Mayonnaise! What???" do not fear, there is no residual mayonnaise taste in these muffins whatsoever. If you think about it, mayo is really just egg whites and vinegar, which often appear together in cake recipes. And these are very cake-y indeed. Even my banana-phobic brother in law couldn't get enough of these. Also, to the reviewer who found the recipe not liquid-y enough, something must have gone horribly wrong. You do have to make sure that you choose bananas that are past their prime, they'll break down into liquid and sugar better/faster. Also, the mayo makes this recipe a little more "sticky" than the typical quickbread batter. Just go with it, you won't be sorry. - 11 Sep 2010 (Review from Allrecipes USA and Canada)
Mix the bananas and mayo together first, then add the dry ingredients. I made it in my KitchenAide mixer - VERY moist - no need to add any other liquid. Oh, delicious!! I'll definitely make again! - 17 Oct 2009 (Review from Allrecipes USA and Canada)