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

Cream together butter, granulated sugar, and brown sugar until light and fluffy using an electric mixer.

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

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

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

Stir in maple syrup until evenly distributed. Drop rounded tablespoons of dough onto prepared baking sheets, leaving 2 inches between cookies.

Bake for 9-11 minutes, or until edges are golden brown. Let cool on baking sheets for a few minutes before transferring to a wire rack to cool completely.

For the icing: Whisk together powdered sugar and maple syrup. Add milk, one tablespoon at a time, until desired consistency is reached. Drizzle or spread over cooled cookies.