Preheat the oven to 350°F (175°C). Line baking sheets with parchment paper or a silicone mat.

In a large bowl, cream the softened butter and brown sugar until smooth and slightly fluffy, about 1 to 2 minutes by hand or 30 seconds with a mixer.

Beat in the 1/4 cup maple syrup and the egg until the mixture is homogeneous and glossy. Add the vanilla and mix briefly.

In a separate bowl, whisk together the 2 cups flour, 1 teaspoon baking soda, and 1/2 teaspoon salt.

Gradually add the dry ingredients to the wet mixture. Stir until just combined; avoid overmixing.

Drop rounded tablespoon-sized balls of dough onto the prepared baking sheet, spacing them about 2 inches apart.

Bake for 10 to 12 minutes, or until cookie edges are lightly golden and centers still look slightly soft.

Remove from oven and let cookies sit on the sheet for 2 minutes, then transfer to a wire rack to cool completely.

For the glaze, whisk together 1 cup powdered sugar with 2 tablespoons maple syrup and 1 tablespoon milk.

Drizzle or spread the glaze over cooled cookies. Let the glaze set for 15 to 20 minutes before stacking or storing.