In a medium bowl, whisk together flour, baking powder, baking soda, and salt
In a large bowl, cream butter and brown sugar until light and fluffy (about 3 minutes)
Beat in egg, maple syrup, and vanilla until well combined
Gradually mix in dry ingredients until just combined
Cover dough and refrigerate for 2 hours
Preheat oven to 350°F (175°C)
Line baking sheets with parchment paper
Scoop chilled dough into 1.5-inch balls, place 2 inches apart
Bake 12-14 minutes until edges are lightly golden
Cool on sheets for 5 minutes before transferring to wire racks
For icing: whisk powdered sugar, maple syrup, milk, and vanilla until smooth
Once cookies are completely cool, spread with maple icing