Preheat oven to 350 degrees. Line cookie sheets with parchment paper.
Cream butter and sugar
Add egg, vanilla and mashed bananas.
Combine dry ingredients and add to banana mixture. (The dough is very soft.)
Drop by tablespoons onto prepared pans.
Bake from 10-12 minutes, just until they are a little brown on the bottom (do not over cook!)
Remove to wire racks and let cool while you make icing.
In a medium sized pot, melt butter with cream and brown sugar.
Bring to a soft boil and add in part of the icing sugar. You want it to start to thicken up. Not too runny but still flows.
Then spoon icing over cookies on the wire racks while the icing is still hot.
Let icing set.