Cream sugar, butter, shortening, and vanilla until light and fluffy.
Add bananas and then mix in the eggs.
Blend in buttermilk. Add the dry ingredients until just combined. Do not over-beat. It will be a sticky batter. Drop by tablespoons onto a greased cookie sheet.
Bake for 9-10 minutes, until slightly golden.
Cool completely.
Frosting
Mix all ingredients together and spread over cooled cookies.
Notes
If you aren’t going to eat them for more than a week, we recommend freezing them. Again the best way to freeze them is placing them in an airtight storage container and putting them in the freezer.