In a large bowl, mix together banana, mayonnaise, egg, and vanilla.
In a medium bowl, whisk together flour, sugar, nuts, baking soda, and salt.
Add flour mixture to banana mixture and stir until just combined.
Bake 60-70 minutes, or until a toothpick comes out clean. Cool for 15 minutes in the pan then place on a cooling rack. Cool completely. Slice and serve!