Preheat the oven to 350°F and grease a 9×5-inch loaf pan.
In a large bowl, mash the bananas until mostly smooth. Set aside.
Chop the Oreos into small pieces and set aside.
In another bowl, combine the melted butter, granulated sugar, brown sugar, egg, and vanilla extract. Whisk until well combined.
Add the mashed bananas and mix.
In a separate bowl, whisk together the flour, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients. Mix until just combined. Do not overmix.
Gently fold in the chopped Oreos.
Pour the batter into the prepared loaf pan and smooth the top.
Sprinkle more chopped Oreos over the top.
Bake for 55–60 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs.
While the banana bread is baking, make the icing. Whisk together the cream cheese, powdered sugar, vanilla extract, and heavy cream or milk until smooth and creamy.
Transfer the icing to a piping bag or zip-top bag. If using a zip-top bag, snip off a small corner.
Remove the banana bread from the oven and let it cool completely before adding the icing.
Pipe the icing over the top, then slice and enjoy!