Heat oven to 350. Line standard 12-cup muffin tin with liners.
In a medium bowl, whisk together sugar and oil. Whisk in bananas, egg, egg yolk, buttermilk, and vanilla extract.
In a small bowl, sift together flour, baking soda and salt. Using a whisk, mix the flour mixture into the banana mixture just until combined. Divide the batter evenly among the muffin cups.
Bake 18 to 20 minutes or until toothpick inserted in centers comes out clean. Transfer cupcakes to wire rack to cool completely.
For frosting, place the white chocolate in a microwave-safe bowl and melt in microwave for 30 second intervals, stirring in between. Set aside to cool for 10 to 15 minutes.
In a medium bowl, cream the butter and cream cheese together until light and fluffy. Add vanilla extract and beat until combined. Add the melted white chocolate and beat until well combined. Add powdered sugar and beat on low speed until well combined. Frost cupcakes as desired.