In a large mixing bowl, beat the butter and dark brown sugar using an electric mixer on high speed. Mix until creamy and smooth. This usually takes about 3–4 minutes.

Add the vanilla extract and mix well until fully combined.

Remove the bowl from the mixer if using a stand mixer. Sift the flour, baking powder, and salt into the butter mixture.

Return the bowl to the mixer and mix on low speed until the dry ingredients are fully incorporated. The dough will feel soft and delicate.

Pour in the milk and mix slowly until the dough comes together. Continue mixing gently until you have a smooth dough.

Place the dough onto plastic wrap. Wrap it tightly and shape it into a log about 1 ½ x 2 ½ inches thick. Refrigerate for at least 3 hours or up to overnight. Chilling helps the cookies keep their shape.

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

Slice the chilled dough into ¼-inch thick rounds. Place them on the cookie sheet, leaving space between each cookie because they will spread.

Bake for 12 to 15 minutes, or until the edges turn golden brown.

Let the cookies sit on the baking sheet for about 6 minutes. Then transfer them to a wire rack to cool completely.

Your homemade Bordeaux cookies are now ready to enjoy!