Couldn't find Grandma Jennie's recipe for Banana Cake, but Marash Girl has been using the following BANANA BREAD recipe to make use of those over-ripe bananas. The result is delicious. If you want a more cake-like product, just add more sugar to the recipe below (2 cups instead of one) and replace some of that canola oil with butter.
Banana Bread Recipe
1/2 cup canola oil
1 cup sugar
3 mashed very ripe bananas (preferably the skin should be mostly black)
1 tsp baking soda
1 tsp baking powder (Marash Martha's recommends using both)
2 cups flour
1/4 tsp salt
4 tsp sour milk (add a smudge of vinegar to milk or use yogurt or flavored yogurt -- if you use flavored yogurt, you'll keep your guests guessing as to the "je ne sais quoi".)
1 or 2 tsps. pure vanilla (not the artificial variety) or lemon flavoring
Beat eggs; add sugar and oil.
Mash bananas well and add to mixture.
Into a separate bowl, sift flour, salt, baking soda/powder.
Make a well in the dry ingredients and add the sour milk and egg/banana mixture. Stir gently until smooth. Do not over beat!
Bake in a greased pan at 350 degrees fahrenheit for about one hour, or until done. (Test with cake tester to make sure batter is firm.)
Cool well before slicing.
Marash Girl's recommendation? Make more than one recipe and share with your neighbors!