Heat oven to 350 degrees. Grease and flour 15x10 inch pan. In a large bowl, beat together sugar, cream cheese, butter and eggs until creamy. Blend in bananas and vanilla extract. In another large bowl, stir together flour, baking soda and salt. Add to egg mixture in thirds and blend for one minute. Stir in walnuts. Spread batter evenly into pan. Bake 20 to 25 minutes or until golden brown. Cut into bars. Meanwhile, for frosting, heat butter in a large sauce pan over medium heat until boiling. Let the butter turn a delicate brown and remove from heat immediately. Add powdered 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).