Preheat oven to 375°F (190°C). Grease a 10"x 15" sheet pan (jelly roll pan) and dust with flour.
Whisk together the flour, baking soda, and salt. Set aside.
Using an electric mixer on medium speed, beat the butter, sugar, and brown sugar until light and fluffy. Add the eggs and vanilla, mixing well. Mix in the sour cream and bananas.
Gradually add the flour mixture, mixing just until combined. Stir in the pecans.
Pour the batter into the prepared pan and spread evenly.
Bake 20-25 minutes, or until golden brown. Place the pan on a wire rack to cool slightly while you prepare the icing.
To make the icing:
Place the butter in a medium saucepan. Melt the butter over medium heat. Continue cooking until butter foams and brown specks begin to form at the bottom of the pan.
Remove from heat. Add about 1 cup of confectioners' sugar, vanilla, and about 1 tablespoon of milk. Stir into the butter. Add the remaining sugar and milk in 2-3 more portions, working quickly to mix well.
Quickly spread the icing evenly over the warm bars. Allow the bars and icing to cool before cutting into bars.
Notes
*The amount of milk you'll need may vary. Use as much as you need to make the icing spreadable. It shouldn't be as thick as frosting, but thicker than a glaze.Â
These banana bars are best stored in the refrigerator, where they’ll keep in an airtight container for up to 5 days. Let them sit at room temperature for a few minutes before serving.