Whisk the flour, baking soda, and salt together in a medium bowl. Set aside.
Using a hand mixer or a stand mixer fitted with a paddle attachment, cream the butter and brown sugar together on medium speed until smooth, about 1-2 minutes.
Add the egg and beat on high until combined, about 30 seconds. Scrape down the sides and bottom of the bowl as needed.
Add the maple syrup, vanilla extract, and maple extract, then beat on high speed until combined.
Gradually add the dry ingredients to the wet ingredients, then mix on low speed until fully combined.
Fold in the chopped pecans, then beat on low speed until evenly distributed. The dough will be creamy and soft.
Cover and chill the dough for at least 2 hours (or up to 3 days). If chilling for longer than a few hours, allow it to sit at room temperature for at least 30 minutes before rolling and baking.
Preheat oven to 350°F (177°C). Line 2-3 large baking sheets with parchment paper or silicone baking mats. Set aside.
Roll the cookie dough into balls, about 1.5 tablespoons of dough per cookie. Place on the prepared baking sheets.
Bake each batch for 12-13 minutes, until lightly browned on the sides. The centers will look very soft.
Remove from the oven and, if needed, lightly bang the pan on the counter to deflate the cookies slightly, creating lovely cracks on the surface.
Allow cookies to cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely.
To make the icing, in a small saucepan over low heat, melt the butter and maple syrup together, whisking occasionally. Once the butter has melted, remove from heat and whisk in the sifted confectioners’ sugar. Taste and add a pinch of salt if desired.
Drizzle the icing over the cooled cookies. Allow the icing to set for about 1 hour.
Store cookies in an airtight container at room temperature for up to 1 week.