In a small saucepan over medium heat, melt the butter and let it come to a simmer. Whisking constantly let the butter simmer until brown specks appear at the bottom of the saucepan and the butter has a rich amber color. Transfer the butter to a bowl and let sit in a cool spot until it has cooled completely and starts to solidify about 30-45 minutes.
In the bowl of a stand mixer fitted with the paddle attachment or using a hand mixer, beat the butter until smooth. Then add sugar, salt, vanilla sugar, and milk. Mix until smooth.
Combine flour and baking powder, and add to the butter mixture with the mixer running on low. Mix until combined.
Turn out the dough onto a lightly floured work surface, then knead the dough by hand, divide it by three and shape each portion into a log with a 1.5-inch diameter.
Roll each log in sugar and wrap it in plastic wrap. Refrigerate for at least 1 hour.
Preheat oven to 350 degrees F (180C) and line a baking sheet with parchment paper.
Cut the logs into 1/4-inch thick slices with a sharp knife and transfer the cookies onto the baking sheet.
Bake cookies for 13-15 minutes in the middle of the oven or until just lightly browned on the edges. Take out of the oven and let cool on a wire rack.