Preheat the oven to 350°F (175°C). Prepare a baking sheet by lining it with parchment paper.

In a large mixing bowl, cream together the butter and granulated sugar until the mixture becomes light and fluffy.

Sequentially add the eggs to the mixture, fully incorporating each one before introducing the next.

Gradually mix in the buttermilk, maintaining a low speed.

Combine the salt, vanilla extract, maple extract, baking soda, and baking powder, and integrate them into the batter.

Methodically add half of the flour into the mixture, ensuring thorough mixing, then incorporate the remaining flour to form a consistent dough.

Use a spoon to place approximately two-tablespoon-sized portions of dough onto the prepared baking sheet, spacing them about two inches apart.

Bake the cookies in the preheated oven for 6 to 8 minutes, taking care to avoid overbaking. The cookies should remain pale in color.

Allow the cookies to cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.

In a saucepan over medium heat, melt the butter and brown sugar, and bring the mixture to a boil for two minutes, whisking continuously.

Add the milk, maple syrup, and a pinch of salt to the saucepan, and bring the mixture back to a boil for one minute, while continuously whisking.

Remove the saucepan from the heat and let the mixture cool for 15 minutes.

Gradually incorporate the powdered sugar, whisking until the icing achieves a glue-like consistency. Adjust the thickness by adding milk, one tablespoon at a time, as needed.

Promptly spread the icing over the cooled cookies, as it will thicken upon cooling. Add more milk if necessary to maintain a spreadable consistency.

Allow the icing to set before storing the cookies in a covered container.