Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a large bowl, cream the butter and brown sugar until light and fluffy.
Beat in the maple syrup, egg, and vanilla extract until smooth.
In a separate bowl, whisk together the flour, baking soda, baking powder, and salt.
Gradually add the dry ingredients to the wet, mixing until just combined.
Scoop tablespoon-sized balls of dough and place on the prepared baking sheet, leaving room to spread.
Bake for 10–12 minutes or until the edges are lightly golden. Let cool completely.
For the icing, whisk together the powdered sugar, maple syrup, and just enough cream or milk to reach a drizzling consistency.
Spoon or dip icing over cooled cookies. Let them set until the icing firms up.