Whisk the flour, baking soda and salt in a medium bowl. Beat the butter and brown sugar in a large bowl with a mixer on medium-high speed until fluffy, about 3 minutes. Beat in the maple syrup, egg, vanilla and maple extract. (The mixture may look curdled.) Reduce the mixer speed to medium low; add the flour mixture and beat until combined. Cover and refrigerate until the dough is no longer sticky, about 30 minutes (it will still be soft).
Position racks in the upper and lower thirds of the oven and preheat to 350 degrees F. Coat 2 baking sheets with cooking spray. Put the turbinado sugar in a shallow dish. Roll tablespoonfuls of the dough into 1-inch balls, then roll in the turbinado sugar. Press a walnut half into the center of each cookie and arrange 2 inches apart on the prepared baking sheets.
Bake, switching the pans halfway through, until the edges of the cookies are set but the centers are still soft, 12 to 14 minutes. Let cool 5 minutes on the baking sheets, then transfer to racks to cool completely.