Preheat oven to 375. Butter or spray an 8x8 or 8.5x11 baking pan and set it aside.
In a large bowl, combine flour, sugar, baking powder, baking soda, cinnamon and salt.
In a medium bowl, whisk yogurt, mashed banana, milk, oil, egg and vanilla until combined.
Pour wet ingredients into the dry ingredients and stir until just combined.
Pour the batter into the prepared pan and bake for 20-25 minutes, until a toothpick inserted into the center comes out clean. If you're using an 8x8 pan the baking time will be closer to 25 minutes. An 8.5x11 pan should be done closer to 20 minutes. Cool the cake completely before topping with frosting.
For the frosting:
Beat cream cheese and butter until combined. Add powdered sugar and beat until smooth and creamy. Using a butter knife or an offset spatula, spread the frosting all over the top of the cooled cake.