Preheat oven to 350 degrees.
In a stand mixer or a large bowl, cream together butter and sugar until light and fluffy. Add egg and vanilla, and beat for 2 minutes.
Mash bananas in a bowl and add to mixing bowl, and beat to combine.
Add flour, baking soda, and salt to mixing bowl and mix well.
Lightly spray the inside of a cookie scoop (I used a 1 1/2 inch size). Scoop dough onto prepared cookie sheet, leaving space between each dough.
Bake for 8-9 minutes until cookies are golden brown on edges and bottom.
Immediately remove cookies from cookie sheet and place on a cooling rack until completely cool.
To make the frosting place 1/2 cup softened butter and 6 TBS brown sugar into a medium bowl and using a hand mixer, blend together until smooth. Add milk and mix. Incorporate powdered sugar one cup at a time until you reach a thick consistency (2-3 cups).
Smooth frosting over the cookies. Enjoy.