Preheat oven to 350 degrees. Grease a round cake pan and set aside.
In a food processor, blend avocado, bananas, egg, vanilla, and milk. If you don't have a food processor, mash the banana and avocado well. Then, whisk all the ingredients together until smooth.
Place mixture into a medium bowl. Add flour, sugar, cocoa powder, and baking soda. Fold just until combined.
Spread cake batter into greased cake pan. Batter will be thick. Spread until the batter is even and to the edges of the pan.
Bake for approximately 24 minutes, or until the center is firm and/or a toothpick inserted into the middle comes out clean.
Allow to cool slightly. Then, flip cake onto a cooling rack so that the top of the cake is against the rack.