Preheat your oven to 350°F and line a baking sheet with parchment paper. This helps prevent sticking and makes cleanup much easier. Set the baking sheet aside while you prepare the dough.
In a large mixing bowl, cream together the softened butter and brown sugar using an electric mixer until the mixture is light and fluffy. This step usually takes 2-3 minutes and is key for creating the right texture in your cookies.
Add the maple syrup, egg, vanilla extract, and maple extract to the bowl. Beat again until everything is well incorporated. The mixture may look slightly separated at first, but it will smooth out as you mix.
In a separate bowl, whisk together the flour, baking soda, baking powder, salt, and cinnamon. Slowly add this dry mixture into the wet ingredients, mixing on low speed until just combined. Overmixing can make your cookies tough, so stop as soon as you no longer see streaks of flour.
Scoop the dough into tablespoon-sized portions and place them on the prepared baking sheet about 2 inches apart. Bake for 9-11 minutes, or until the edges are just starting to turn golden. They may look slightly underbaked in the center, but they will set as they cool.
Transfer cookies to a cooling rack and let them cool completely before glazing. For the glaze, whisk together the powdered sugar, maple syrup, and enough milk to reach a smooth, pourable consistency. Drizzle or spread over the cooled cookies and let the glaze set before serving.