In a small saucepan set over medium heat, brown the butter. Stir the butter occasionally until it turns amber in color and develops little brown specks.
Transfer the butter to a small bowl and set it in the freezer for 5 minutes to chill.
Banana Cake
Preheat the oven to 350°F / 175°C. Butter a 7" springform pan, then coat it with sugar.
In a medium sized mixing bowl, mash up the banana until no large chunks remain.
Add in 90g of the brown butter. Leave the remaining brown butter out at room temperature until you're ready to make the frosting.
Add in the sugar, egg, vanilla, and sour cream. Whisk vigorously until the mixture is well combined.
Add in the flour, baking powder, salt, and cinnamon. Whisk together until only a few flour streaks remain. Add in the chopped pecans, then mix just until no flour streaks remain.
Pour the cake batter into the prepared cake pan. Bake for 35-40 minutes, or until a toothpick inserted in the center of the cake comes out clean.
Salted Caramel Cream Cheese Frosting
Add the cream cheese and remaining brown butter to a medium sized mixing bowl. Use a hand mixer (or stand mixer fitted with the paddle attachment) to beat the ingredients together until the mixture is light and fluffy (1-2 min.)
Beat in the powdered sugar until well combined, then add in the salted caramel sauce and beat for an additional minute.
Once the cake has fully cooled to room temperature, top it with the cream cheese frosting. Swirl some more salted caramel sauce on top, then slice, serve, and enjoy!