Preheat the oven to 375°F. Line two large baking sheets with parchment paper or silicone baking mats and set aside.

In a large mixing bowl, cream the softened butter, brown sugar, and granulated sugar with an electric mixer on medium speed until light, fluffy, and well combined, about 1 to 2 minutes.

Add the mashed banana, egg, and vanilla extract. Beat on medium speed until fully incorporated and smooth.

In a separate medium bowl, whisk together the flour, cinnamon, baking powder, baking soda, nutmeg, and salt.

Gradually add the dry ingredients to the wet ingredients, mixing on low speed just until a soft, sticky batter forms. Do not overmix. Scrape down the sides and bottom of the bowl as needed.

Using a medium cookie scoop, drop rounded scoops of batter onto the prepared baking sheets, spacing them about 3 inches apart.

Bake for 7 to 9 minutes, or until the tops are set, the edges are lightly golden, and a toothpick inserted into the center comes out clean.

Let the cookies cool on the baking sheets for 5 to 10 minutes, then carefully transfer them to a wire rack to cool completely.

To make the frosting, beat the softened cream cheese on medium speed until smooth and free of lumps.

Add the softened butter and beat until well combined and creamy.

Gradually add the sifted powdered sugar and vanilla extract, beating on low speed until incorporated.

Increase the speed to medium-high and beat for 1 to 2 minutes until the frosting is light, fluffy, and spreadable.

Once the cookies are completely cool, spread a generous layer of cream cheese frosting over each cookie. Serve immediately or store as directed.