Preheat oven to 350 degrees F.
Grease an 8.5 x 4.5-inch loaf pan with non-stick spray and set aside.
Add 1/4 cup unsalted butter and sugars into a large bowl and beat on medium-high speed until creamy and lighter in color, about 2-3 minutes.
Add vegetable oil, egg, egg white, vanilla, and beat on medium speed. Scrape the sides and bottom of the bowl with a rubber spatula as needed.
Add in baking powder, baking soda, salt, and half of the flour. Mix on a low speed until just combined.
Beat in 1/3 cup of buttermilk on low speed until incorporated.
Add in the remaining flour and mix on low just until combined. Follow with the remaining buttermilk.
Mix in the mashed bananas at low speed until fully incorporated into the batter.
Fold in the chopped Oreos.
Pour the batter into the prepared pan.
Bake on the middle rack for 55-60 minutes, rotating the pan halfway through. If you notice the top of the loaf is browning quickly, cover the loaf pan with a foil tent.
Remove the loaf from the oven, and let it cool in the pan for 10 minutes after which transfer to a cooling rack. Let it completely cool before adding the glaze.