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

Whisk together all-purpose flour, baking soda, cornstarch, and salt in a separate bowl, then gradually add to the wet ingredients.

Chill the dough in the refrigerator for at least 1 hour, preferably overnight.

Preheat the oven to 350°F (175°C) and roll the dough into 1.5-inch balls, spacing them out on a baking tray.

Bake for 10-12 minutes until lightly golden, keeping the centers soft.

Cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.

Prepare the glaze by whisking together powdered sugar, maple syrup, melted butter, and milk until smooth.

Drizzle the glaze over the cooled cookies and let it set before serving.