Heat oven to 375 degrees F. Grease and flour a 15 x 10-inch jellyroll pan.
For the bars, in a large bowl, beat together sugar, sour cream, butter,
and eggs until creamy. Blend in bananas and vanilla extract. Add flour,
baking soda, salt, and blend for 1 minute. Stir in walnuts.
Spread batter evenly into pan. Bake for 20 to 25 minutes or until golden
Meanwhile, for frosting, heat butter in a large saucepan over medium
heat until boiling. Let the butter turn a delicate brown and remove from
Add confectioners' sugar, vanilla extract and milk. Whisk together until
smooth (it should be thicker than a glaze but thinner than frosting). Using
a spatula, spread the brown butter frosting over the warm bars (the frosting
will be easier to spread while the bars are still warm).