For the Cake
Preheat oven to 350 degrees F. Lightly butter three 8-inch-diameter cake pans with 2-inch-high sides; dust pans with flour. In a medium bowl, combine cake flour, baking soda, baking powder and 1/2 teaspoon salt. Mix mashed bananas, buttermilk and 1 teaspoon vanilla in another medium bowl. Using electric mixer, beat 1/2 cup butter and sugar in large bowl until blended. Add eggs, one at a time, beating to blend after each addition. Add dry ingredients alternately with banana mixture in 3 additions, beginning and ending with dry ingredients and beating just until blended after each addition. Divide batter equally among prepared pans.
Bake cakes until tops are just beginning to color and tester inserted into center comes out with a few crumbs attached, about 20 minutes. Cool cakes in pans on racks 10 minutes. Using small knife, cut around cakes to loosen; turn cakes out onto racks and cool completely.
For the Frosting
Beat cream cheese and remaining 1 cup butter in large bowl until light and fluffy. Beat in remaining 1 tablespoon vanilla and pinch of salt. Gradually beat in powdered sugar. Cover and refrigerate frosting until firm enough to spread, about 15 minutes.
Place 1 cake layer on platter. Spread 1/2 cup frosting over top. Place half of sliced bananas evenly over frosting, leaving 1/4-inch border at edge. Place second cake layer on work surface. Spread 1/4 cup frosting over top. Place cake layer, frosting side down, atop bananas. Spread 1/2 cup frosting over top. Place remaining half of sliced bananas evenly over frosting, leaving 1/4-inch border at edge. Place third cake layer on work surface. Spread 1/4 cup frosting over top. Place cake layer, frosting side down, atop bananas. Spread remaining frosting over sides and top of cake. (Can be made 1 day ahead. Cover and chill. Let stand 1 hour at room temperature before serving.)