Preheat oven to 350F degrees. Line 8x8" square pan with foil.
Make the cake. Mix together flour, baking soda, cinnamon and salt in a small bowl. Set aside.
Using a handheld or stand mixer with a paddle attachment, cream together butter and sugars on medium speed until smooth (I did this by hand using a wired whisk). Add egg, mix well. Add vanilla and banana, mix until well combined.
Mix in half of the flour mixture, then the sour cream, then the remaining flour mixture. Mix just until combined and you can no longer see clumps of flour. Do not over-mix.
Pour batter into the pan. The batter is quite thick (like a banana bread batter) so try to spread it evenly. Bake for 11 to 13 minutes or until the sides start to puff-up and the top starts to brown a little. Don't let the top brown too much or the cake will become dry. I took out mine from the oven at 13 minutes, but the cake turned out a little dry so try to check it at 11 or 12-minute mark. Let the cake cool completely.
Make the frosting. Using a handheld or stand mixer with a paddle attachment, beat cream cheese and butter on medium speed, about 2 minutes. Add the confectioners' sugar by starting from 1/4 cup, then sift above the bowl*. Beat until combined. Add the remaining powdered sugar, sift above the bowl, then beat very well. The frosting might look crumbly or gritty but don't worry, it will become smooth as you beat it. Add the vanilla, beat until combined. Add more confectioners' sugar if you want to make it more sweet.
Put dollops of cream cheese frosting all over the cake then spread evenly, especially on the sides. Place the frosted cake in the refrigerator for 30 mins to 1 hour to let the cream cheese set up a bit so it can be sliced easily. If the frosting had firmed up, cut it into 16 squares. Bring to room temperature before serving. Enjoy!
Notes
• The cinnamon is a little bit strong here. You can reduce it to 1/4 teaspoon.
• I reduced the amount of sugar by half. It is still a bit sweet but it's fine especially if you will not serve it with the cream cheese frosting. You may reduce the white sugar by 1/2 tablespoon if you really want to cut back the sweetness.
• Measure the egg - crack egg into a small bowl, beat with fork, then measure out using a food scale. Or just use 1 medium to large egg.
• Measure the bananas - peel the skin of the bananas, mash with fork then measure the required amount using a food scale. Or just use 3 medium bananas.
• Measure unsifted confectioners' sugar, then sift - the reason why I do this method is because I want to control the sweetness of the frosting. I start from 1/4 cup, then add little by little until my desired sweetness is achieved. I also find it a bit convenient to sift the confectioners' sugar into the bowl of the cream cheese/butter mixture. If you are hesitating to do this, you may definitely sift the sugar on a separate bowl BUT still measure it while it is unsifted. REASON: unsifted and sifted powdered sugar have different volume and density. If you measure SIFTED sugar in this recipe, you will end up having more sugar and of course, sweeter frosting.
• Store in an airtight container or in a baking pan covered with foil in the refrigerator. I stored it in a baking pan uncovered for 3 days and had no problems with it. Bring to room temperature before serving (I prefer this than serving it cold because the cake softens and the frosting becomes creamy again.