Preheat your oven to 375°F (190°C) and line an 8x8 inch baking dish with parchment paper.

In a mixing bowl, combine softened butter, sugar, sour cream, and egg. Blend until smooth and creamy. Fold in mashed bananas and vanilla extract.

Whisk together flour, baking soda, and salt in a separate bowl. Gradually stir the dry mixture into the banana mixture until just combined.

Pour the batter into your prepared baking dish and bake for 20-25 minutes, until golden brown and a toothpick comes out clean.

Allow the banana bars to cool in the baking dish for about 10 minutes, then lift them out using the parchment and cool completely on a wire rack.

In a saucepan, melt the butter over medium heat and swirl it until it turns golden brown and develops a nutty aroma.

Whisk in powdered sugar and vanilla extract until smooth. If too thick, add milk gradually until desired consistency is reached.

Spread the frosting generously over the cooled banana bars and allow to set before cutting into squares. Serve at room temperature or slightly warm.