Mix butter and sugar: Put the sugar and softened butter in a big bowl. Use an electric mixer (handheld or stand mixer) to beat them together for a few minutes until they look light and fluffy.

Add the wet stuff: Crack the egg into the bowl. Add the vanilla extract and mashed bananas. Beat everything together until it's well mixed.

Mix the dry stuff: In a separate bowl, mix the flour, salt, baking soda, baking powder, and cinnamon. Stir them together with a whisk or fork.

Combine everything: Add half of the dry ingredients to the banana mixture. Then, pour in half of the buttermilk. Mix until just combined. Don't overmix! Now, do it again: add the rest of the dry ingredients and the rest of the buttermilk. Mix until just combined.

Cool down: Let the cake cool completely in the pan before you put the frosting on.

Brown the butter: Put the butter in a small saucepan over medium heat. It will melt and then start to foam. Keep stirring! The foam will go away, and you'll see little brown bits at the bottom of the pan. That's browned butter! Be careful not to burn it. Take it off the heat as soon as you see the brown bits.

Make the icing: Pour the browned butter into a bowl. Add the powdered sugar and vanilla bean paste (or extract). Stir it all together until it's smooth and creamy.

Frost the cake: Once the cake is completely cool, pour the icing over the top. Spread it around evenly.

Add caramel (optional): If you want, drizzle some caramel sauce over the frosting.