Combine the flour, baking soda, and salt in a small bowl and set aside.
In a large bowl, cream the softened butter and brown sugar together with a hand mixer or stand mixer until fluffy.
Beat in the egg, maple syrup, vanilla, and maple extract.
Stir in the flour mixture until combined.
Drop by tablespoon onto an ungreased or parchment paper-lined baking sheet with about 2 inches between each to allow for spreading.
Bake in a preheated oven for 10-12 minutes until set around the edges but still slightly soft in the middle.
Remove from oven and let cookies cool on a wire rack.
While the cookies cool, combine the icing ingredients of melted butter, powdered sugar and maple syrup. Stir until smooth. If needed you can add in a drop or two of water or another teaspoon of powdered sugar to achieve a thick consistency that will still drizzle from a spoon.
Drizzle icing over the cookies. I move them back to the parchment-lined baking sheet to do this for easy cleanup.
Notes
Store cookies covered in an airtight container at room temperature for up to 4 days.