Preheat the oven to 350°F (175°C). Grease and flour a 9×13 inch baking pan.

In a large mixing bowl, beat together the mashed bananas, sugar, and butter until creamy. Add the eggs and vanilla extract, mixing until well combined.

In a separate bowl, whisk together the flour, baking powder, baking soda, and salt.

Gradually mix the dry ingredients into the wet mixture until just combined. Be careful not to overmix; a few lumps are perfectly fine.

Pour the batter into the prepared pan, spreading it evenly. Bake for 20-25 minutes, or until a toothpick inserted in the center comes out clean.

Allow the bars to cool in the pan for about 10 minutes before transferring to a wire rack to cool completely.

In a saucepan, melt the butter over medium heat. Stir in the brown sugar and bring it to a boil, continuing to stir for 2 minutes.

Remove from heat and add the heavy cream and salt, stirring until smooth.

Once the bars are completely cool, beat in the powdered sugar until the frosting reaches your desired consistency. Spread generously over the cooled banana bars, and sprinkle with extra sea salt if desired.