In a medium bowl add the dry ingredients - flour, baking soda and salt. Whisk to combine and set aside.
Whisk butter and brown sugar until smooth, about 1-2 minutes. Scrape the sides of the bowl with a spatula as needed. Add the egg and beat until combined, about 30 seconds. Add maple syrup, vanilla extract and mix until combined, about 30 seconds.
Add the dry ingredients in 2 batches over the wet ingredients and mix until combined. The dough will be soft and creamy.
Cover and chill for at least 2 hours, up to 3-4 days. Let it thaw 30 minutes before rolling, because the dough will be hard to work with.
Preheat oven to 180°C and line 2 or 3 large baking sheets with parchment paper.
Divide dough in half, roll, cut in the desired shape or form into a ball and bake for 12-14 minutes or until lightly browned on the sides. Remove from the oven, let them cool on the baking sheets for 5 minutes before transferring to a wire rack to cool completely.
To make the icing: Add butter and maple syrup to a small pan over low heat. Whisk occasionally until the butter has melted. Turn off heat and whisk in the sifted powdered sugar and vanilla extract. Add a pinch of salt if needed. Drizzle over cooled cookies. The icing will set after about 1 hour.
Keep the cookies covered at room temperature and enjoy.