Preheat your oven to 350°F and grease a 13x9-inch baking dish.
In a small bowl, beat the egg whites until soft peaks form; set aside.
In a large bowl, cream together the shortening and sugar until light and fluffy.
Add the egg yolks and mix until well incorporated, followed by the mashed bananas.
In another bowl, combine the flour and baking soda. Add this to the creamed mixture alternately with buttermilk, mixing after each addition.
Stir in the vanilla extract and gently fold in the beaten egg whites to keep the batter airy.
If desired, fold in the chopped walnuts for extra texture and flavor.
Pour the batter evenly into the prepared baking dish and smooth out the top.
Bake for 45-50 minutes, or until a toothpick inserted in the center comes out clean. The top should be golden brown.
Allow the squares to cool on a wire rack. Optionally, top with whipped cream and banana slices before serving.