Preheat oven to 375°F (190°C). Line baking sheets with parchment paper.

In a large bowl, cream together the softened butter, granulated sugar, and brown sugar until light and fluffy. Use an electric mixer for best results.

Beat in the eggs one at a time, then stir in the vanilla extract.

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

Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Do not overmix.

Stir in the maple syrup until evenly distributed.

Drop rounded tablespoons of cookie dough onto the prepared baking sheets, leaving about 2 inches between each cookie.

Bake for 9-11 minutes, or until the edges are golden brown.

Let the cookies cool on the baking sheets for a few minutes before transferring them to a wire rack to cool completely.

While cookies cool, whisk together powdered sugar and maple syrup in a small bowl. Add milk, one tablespoon at a time, until desired consistency is reached. Drizzle or spread icing over cooled cookies.