Preheat the oven to 350F. Grease and line an 8x8” square baking pan with parchment paper, allowing some to hang off the sides. Set aside.
Add the butter to a saucepan over medium-high heat. Allow to melt and slightly brown, while stirring continuously (~5-8 minutes). Remove from heat and set aside to cool slightly.
Continue making the banana cake batter. In a medium bowl, whisk together the flour, baking soda, salt, and cinnamon. Set aside.
In a separate large bowl, combine the slightly cooled brown butter and both sugars. Whisk to combine until smooth.
Then, add in the eggs, yogurt, mashed bananas, and vanilla. Whisk until well combined.
Add the dry ingredients to the wet, and mix until just combined.
Pour the batter into the prepared pan and spread.
Bake at 350F for 45-55 minutes, until a deep golden brown and a toothpick inserted into the middle comes out clean. If the cake starts to brown too much but isn’t fully done in the center, tent the pan with foil in the last 15 minutes of baking.
While the cake is cooling, make the cream cheese frosting. In a medium bowl, beat together the cream cheese and butter until smooth. Then, add the vanilla and powdered sugar, and beat until well combined, smooth and fluffy. Set aside.
Make the salted caramel sauce by combining all of the ingredients in a medium bowl, and mixing until well combined and smooth. You can adjust the runniness to your liking by adding more maple syrup, if needed.
Once the cake is COMPLETELY cooled, spread the frosting onto the cake in an even layer.
Then, dollop the salted caramel all over the top, and use a spoon to swirl it into the frosting.
Top with a little bit of flaky sea salt. Cut into 16 slices.
