Preheat oven to 350 degrees F
In a medium-sized bowl, whisk together flour, baking powder, baking soda, and salt.
In a large bowl, beat together sugar, mayo, and vanilla.
Mix the flour mixture into the wet mixture in thirds alternating with cold water. Blend well. Divide batter evenly among cupcake tins lined with cupcake papers.
Bake for 22-24 minutes or until a toothpick comes out clean.
Cool cupcakes in tin on a wire rack for 3 minutes. Then tip them out of the tin onto the wire rack to finish cooling. When the cupcakes are cooled completely, frost them as desired.
