Brown the Butter: Start by heating the butter in a pot over medium heat until it turns golden brown and releases a nutty aroma. Avoid burning it; keep a close eye on the color change.

Create the Mixture: Once the butter has cooled to a soft consistency, mix in the powdered sugar, milk, and vanilla extract. The combination should be smooth and creamy without any lumps.

Form the Dough: Gradually incorporate the flour and salt into the mixture, stirring well until a soft dough forms. Be careful not to overwork it, or the cookies will lose their tender texture.

Chill the Dough: Shape the dough into a log about 4 cm thick, wrap it tightly in plastic wrap, and chill it in the refrigerator for at least one hour.

Preheat the Oven: Preheat your oven to 180°C (350°F) and line baking sheets with parchment paper to prevent sticking.

Shape and Bake: After chilling, roll the dough log in coarse sugar and cut it into 1 cm thick rounds. Place them on the prepared baking sheets and bake until the edges are lightly golden, which should take about 10-12 minutes.