Preheat your oven to 350°F (175°C) and line two baking sheets with parchment paper.

In a medium bowl, whisk together the all-purpose flour, baking soda, ground cinnamon, ground nutmeg, and salt.

In a large mixing bowl, beat the softened butter with granulated sugar and brown sugar until light and fluffy.

Add the egg and vanilla extract to the creamed mixture, mixing until fully combined.

Stir in the mashed ripe bananas until well incorporated.

Gradually fold in the dry ingredients mixture into your wet ingredients using a spatula.

Drop tablespoon-sized dollops of dough onto the prepared baking sheets, spacing them about 2 inches apart.

Bake for 10 to 12 minutes, or until the edges are lightly golden while the centers may still look soft.

Let the cookies cool on the baking sheets for about 5 minutes before transferring to a wire rack.

For icing, whisk together powdered sugar, milk, and vanilla extract until smooth, and drizzle over cooled cookies.