Preheat your oven to 375°F (190°C) and line two large baking sheets with parchment paper. In a medium bowl, whisk together the flour, baking soda, salt, cinnamon, and nutmeg or allspice.

In a large mixing bowl, cream together the softened butter, granulated sugar, and brown sugar until light and fluffy, about 2–3 minutes. The brown sugar is key for chewiness.

Beat in the egg and vanilla extract until fully combined. Mix in the mashed bananas. The mixture may look curdled, but that's okay.

Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Do not overmix. Fold in walnuts or pecans if using.

Drop rounded tablespoons of dough onto the prepared baking sheets, spacing 2 inches apart. Bake for 8–10 minutes, or until edges are lightly golden and centers are set but soft.

Let cookies cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.

While cookies cool, beat softened cream cheese and butter together until smooth and lump-free.

Gradually beat in powdered sugar, one cup at a time. Add vanilla extract and milk or cream, adjusting for a stiff, pipeable consistency.

Flip half the cooled cookies upside down. Pipe or spoon frosting onto the flat side. Top with remaining cookies, pressing gently. Chill for 30 minutes before serving.