I found this in a Goodhousekeeping Cookbook I have and my daughter who is visiting me was nice enough to type it in.

BANANA CAKE

2 1/4 cups cake flour
1 1/4 cups sugar
1 1/2 cups well-mashed ripe bananas (3 to 4)
1/2 cup shortening
2 eggs
2 1/2 teaspoons double-acting baking powder
1 teaspoon vanilla extract
1/2 teaspoon baking soda
1/2 teaspoon salt

Early in Day:
Preheat oven to 375F. Grease and flour two 8-inch round cake pans. Into large bowl, measure all ingredients; with mixer at low speed, beat until well mixed, constantly scraping bowl with rubber spatula. Beat at high speed 5 minutes, occasionally scraping bowl. Pour batter into pans and bake 25 minutes or until toothpick comes out clean. Cool layers in pans on wire racks 10 minutes; remove from pans and cool on racks. Makes 2 layers.

Fill and frost cake with:

Whipped-Cream Frosting
2 cups heavy or whipping cream
1/4 cups confectioners' sugar
dash salt
1 teaspoon vanilla extract
In a small bowl, with mixer at medium speed, beat cream with sugar and salt until stiff peaks form; fold in vanilla. Keep frosted cake in fridge until serving time. Garnish with thin slices of banana that have been dipped into lemon juice.

OR...fill and frost with:

Butter-Cream Frosting
1 16-ounce package confectioners' sugar
6 tablespoons butter or margarine, softened
3 to 4 tablespoons milk or half-and-half
1 1/2 teaspoons vanilla extract
1/8 teaspoon salt
In a large bowl, with mixer at medium speed (or with spoon), beat all ingredients until very smooth, adding more milk if necessary to make of good spreading consistency.

--from The Good Housekeeping Cookbook, (c)1973.