Preheat your oven to 350°F. Line a baking sheet with parchment paper.
In a large bowl, combine the mashed bananas and softened butter. Stir in the granulated sugar and brown sugar until smooth. Beat in the egg and vanilla extract.
In a separate bowl, whisk together the all-purpose flour, quick oats, baking soda, baking powder, and salt. Gradually mix the dry ingredients into the wet ingredients until just combined. If the mixture is too wet to hold shape when scooped, add 1 tablespoon more of flour at a time until it firms up. Avoid overmixing.
Drop rounded tablespoonfuls of dough onto the prepared baking sheet, spacing them about 2 inches apart.
Bake in the preheated oven for about 10 minutes or until the edges are lightly golden. Remove from the oven and let the cookies cool on the baking sheet for 10 minutes, then transfer them to a wire rack to cool completely.
While the cookies cool, prepare the glaze. In a small bowl, beat the cream cheese with the powdered sugar and milk until smooth. Drizzle the glaze over the cooled cookies and sprinkle with nuts if using. Enjoy!