Preheat & Prep: Preheat your oven to 350°F (175°C). Line two baking sheets with parchment paper or silicone baking mats.
Cream Butter & Sugar: In a large bowl or stand mixer, cream the softened butter and granulated sugar together until light and fluffy (about 3-4 minutes).
Add Wet Ingredients: Beat in the eggs one at a time, mixing well after each addition. Turn the mixer to low speed and slowly pour in the buttermilk, maple extract, and vanilla extract.
Add Dry Ingredients: Add the baking soda, baking powder, and salt. Mix until combined. Gradually add the all-purpose flour in two batches, mixing on low speed until a consistent dough forms. Do not overmix.
Bake: Use a cookie scoop to drop mounds of dough onto the prepared baking sheets, leaving 2 inches of space between them. Bake for 6 to 8 minutes, just until the edges are slightly golden. Do not overbake.
Cool: Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.
Make the Icing: In a saucepan over medium-high heat, melt the ½ cup of butter and brown sugar, stirring constantly. Stir in the milk, pure maple syrup, and a pinch of salt. Remove from heat and let the mixture cool for 10 to 15 minutes.
Finish the Icing: Gradually whisk the sifted confectioners' sugar into the cooled butter mixture until smooth. (If the icing is too thick, add a single drop of milk at a time to reach your desired consistency).
Frost: Working quickly, spread a generous dollop of icing over each cooled cookie. The icing will thicken and set rapidly as it cools.
Store: Allow the icing to set completely before transferring the cookies to an airtight container. Enjoy!