Preheat oven to 375°F. Line 2 cookie sheets with parchment paper and set aside.
Cream brown sugar and shortening until light and fluffy. Add in mashed bananas and eggs and mix again.
In a separate bowl, whisk together all dry ingredients.
Add 1/3 of the dry ingredients to the banana mixture, then stir. Add remaining flour in 2 more intervals, stopping to stir ingredients together between additions. Dough will be very soft; more like a thick pancake batter.
Scoop dough in 1.5 TBSP balls onto prepared cookie sheet. Cookies will spread, so place only 10 scoops of dough on each sheet. Bake for 10-12 minutes. Let cool for about 5 minutes on the pan before transfering to a cooling rack. Cookies will be soft.
Prepare the icing while baking batches of cookies. Whisk melted butter, vanilla extract and hot water together, then add powdered sugar. Add more hot water as needed to get a smooth, spreadable consistency. Icing should be thick enough to not run off cookies altogether, but instead spread and cover the cookies nicely.
Spoon icing on cooled cookies. Let cool to set. Enjoy!