2 1/4 cups sifted non-self rising cake flour
5 tablespoons all-purpose flour
1 1/2 teaspoons baking soda
1/2 teaspoon salt
1 cup plus 2 tablespoons buttermilk, at room temperature
3/4 cup mashed banana (about 2 very ripe bananas)
10 tablespoons (1 1/4 sticks) unsalted butter at room temperature
6 tablespoons vegetable oil
3/4 cup (lightly packed) light brown sugar
3/4 cup granulated sugar
1 teaspoon vanilla
3 large eggs, at room temperature
Cream Cheese Frosting
Preheat the oven to 350 degrees Fahrenheit. Grease a 13x9-inch baking pan. Sift both flours, the baking soda, and salt together into a small bowl and set aside.
In a second bowl, stir the buttermilk into the mashed banana and set aside.
Cream the butter, oil, both sugars, and vanilla in a medium-size mixing bowl with an electric mixer on medium speed until light and fluffy, about 2 minutes. Scrape te bowl with a rubber spatula.
Add the eggs one at a time to the butter mixture and mix on medium speed after each addition until blended. Scrape the bowl each time.
Add one-third of the dry ingredients with the mixer on low speed, and mix for 8 seconds. Scrape the bowl. Add half the banana mixture, mix for 10 seconds, scrape the bowl. Add the rest of the dry ingredients and the rest of the banana mixture and mix for 10 seconds. Scrape the bowl and stir the batter by hand to mix thoroughly.
Pour the batter into the prepared pan. Bake on the center rack until the top is golden, springs back to the touch, and a tester inserted in the center comes out dry, 30 to 35 minutes. Place the cake on a rack to cool completely.
Frost with Cream Cheese Frosting and refrigerate until ready to serve.
