Preheat oven to 350 degrees. In a mixing bowl whisk together flour, cornstarch, baking soda and salt. In the bowl of an electric stand mixer fitted with the paddle attachment, cream together sugar, butter and 1 Tbsp of the vegetable oil until pale and fluffy.
Mix in remaining 1 Tbsp vegetable oil. Mix in egg then blend in egg white. Stir in mashed bananas.
Working in three separate batches, beginning and ending with flour mixture, add 1/3 of the flour mixture alternating with half of the buttermilk and mixing just until combine after each addition.
Pour batter into 12-paper lined muffin cups, filling each about 2/3 full. Bake in preheated oven until toothpick inserted into center of cupcakes comes out clean, 20 - 25 minutes.
Allow to cool completely then frost with Salted Caramel Peanut Butter Frosting. Store in an airtight container. Drizzle tops with caramel sauce just before serving.
In the bowl of an electric stand mixer fitted with the paddle attachment, whip butter, peanut butter and salt on medium-high speed until pale and fluffy, about 3 minutes, occasionally scraping down sides and bottom of bowl.
Blend in powdered sugar and add enough half and half to reach desired consistency, then whip mixture on medium speed until pale and fluffy, about 3 minutes.
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