Whisk together the flour, baking soda, and salt in a bowl.
In a separate bowl, cream the softened butter and brown sugar until combined. Mix in the egg and maple syrup.
Gradually add the dry ingredients and mix until a dough forms.
Cover and chill the dough for at least 3 hours, or ideally overnight.
Once chilled, let the dough sit out briefly to soften just enough to work with. Divide into portions and roll into balls, handling the dough as little as possible.
Bake at 350°F (175°C) for 12–13 minutes, or until the edges are set. Allow the cookies to cool.
For the icing, melt the butter and maple syrup together in a saucepan. Remove from the heat, then whisk in the sifted confectioners’ sugar and a pinch of salt until smooth. Drizzle over the cooled cookies.
