Cream together the butter and brown sugar until light and fluffy. Beat in the egg, vanilla extract, and maple syrup until smooth.

Whisk together flour, baking soda, cornstarch, and salt. Gradually fold the dry ingredients into the wet mixture.

Cover the dough with plastic wrap and refrigerate for at least 1 hour.

Preheat your oven to 350°F. Roll the chilled dough into balls and place them on lined baking sheets. Bake for 10-12 minutes.

Allow cookies to rest on the sheets for 5 minutes, then transfer to a wire rack to cool completely.

Whisk together powdered sugar, maple syrup, melted butter, and milk until smooth. Drizzle over cooled cookies.