In a large mixing bowl, whisk together flour, cinnamon, nutmeg, baking powder, and salt. Set aside.
In a separate large mixing bowl, beat butter with an electric mixer until light and fluffy, about two minutes. Beat in brown and granulated sugars, followed by the maple syrup. Beat in the egg and vanilla.
Turn the mixer to low, and add the dry ingredients in three installments, stopping frequently to scrape the bowl.
Divide dough in half. Wrap each half in plastic wrap and flatten into a disc. Chill for at least 2 hours or up to 3 days.
Preheat oven to 350F. Line two baking sheets with parchment paper.
Remove dough from the refrigerator. Scoop dough by the tablespoon and roll each into a ball. Place dough balls at least 2 inches apart on prepared pans. Use the back of a very small spoon to press a well into each dough ball.
Bake cookies 12-13 minutes, rotating top-to-bottom and front-to-back. Cookies are done when puffed and no longer wet-looking.
When you remove the cookies from the oven, press the back of a small spoon into the centers again. Let cookies cool on the pans for 10 minutes before carefully removing to a rack to cool completely.
In a small mixing bowl, whisk together confectioner’s sugar, salt, maple syrup, and 3 teaspoons of water until smooth. Add more water if needed.
Transfer icing to a piping bag and fill wells in cookies as desired. Icing will set after a few hours.
