Preheat oven to 350°F (177°C). Grease a 9x13 inch baking pan and set aside.
Mash the ripe bananas until mostly smooth. Measure exactly 1.5 cups and set aside.
In a bowl, whisk together flour, baking powder, baking soda, cinnamon, and salt.
In a large bowl, beat butter until smooth. Add white sugar and brown sugar. Beat until light and creamy.
Add eggs one at a time, mixing well after each addition. Stir in vanilla extract.
Mix in mashed bananas until combined.
On low speed, alternate adding dry ingredients and buttermilk, beginning and ending with dry ingredients. Mix just until combined.
Spread batter evenly into prepared pan. Bake 45 to 50 minutes, or until a toothpick inserted in the center comes out clean.
Cool completely in the pan on a wire rack before frosting.
For the frosting, beat cream cheese and butter until smooth. Add powdered sugar, vanilla, and salt. Beat until fluffy. Adjust thickness with extra powdered sugar if needed.
Spread frosting over cooled cake. Chill for 30 minutes before slicing for clean cuts.