Preheat oven to 375°F (190°C). Grease a 10x15-inch baking sheet.
Mix sugar, sour cream, butter, and eggs until creamy. Incorporate mashed bananas and vanilla.
Combine flour, baking soda, and salt with wet ingredients until just mixed.
Spread batter in prepared pan and bake for 20-25 minutes.
For the glaze: Brown butter in a saucepan until golden. Remove from heat and whisk in remaining ingredients until smooth.
Pour warm glaze over slightly cooled bars and let set before cutting.