Preheat oven to 350. Grease and line 2 8" cake pans.
Whisk dry ingredients together and set aside.
Add banana, sugar, oil and butter to the bowl of a standing mixer and beat until smooth and creamy.
Add eggs one at a time, beating until fully combined.
Add yogurt and vanilla and beat one more time until the batter is homogeneous.
Add dry to wet on low speed. Gradually increase speed to medium-high. Scrape down the bowl as needed.
Use an ice cream scoop to equally divide batter into the pans. I put 7 heaping scoops of batter in both pans and divided the remaining into the pans.
Smooth out the top with an offset spatula.
Bake for 32-35 minutes until a toothpick comes out clean and the top of the cake turns slightly golden brown.*
Place cake pans on a wire rack. Use a knife to go around the cake pans, separating the cake from the side of the pan. Let the cakes cool in the pans for 10 minutes.
Once the cake has cooled, make the icing.
Place butter in a clean bowl of a stand mixer. Beat butter for 2 minutes.
Add 2 cups of icing sugar, 1 tbsp of cream, vanilla and salt. Beat again and add the last cup of icing sugar. If the icing looks dry, add a splash more cream.
This makes ample frosting for a lightly frosted cake.*