Mix butter, 1- quarter cups granulated sugar, egg yolk and vanilla together in bowl with electric mixer until light and fluffy. Add buttermilk and banana. Mix well. Sift together flour, cocoa, baking powder, baking soda and salt. Gradually add flour mixture to batter. Mix until very smooth. Beat egg whites in clean bowl until foamy. Gradually add remaining quarter cup granulated sugar and continue beating until whites are soft and moist, yet hold their peaks. Gently fold whites into batter. Transfer batter to greased and lightly floured 23 cm square cake pan. Smooth surface with spatula. Bake on center oven rack at 350 until wood pick inserted in center comes out clean, about 1 hour. Let cool on rack at least 30 minutes. Shake powdered sugar through a fine sieve over cake before serving (it tastes best when served the day it's baked). Note: because the batter is heavy, the cake bakes more quickly around the edges and is slightly lower in the center. Makes 8 servings. From The Los Angeles Times ----