Brown the butter: In a saucepan, melt the unsalted butter over medium heat, stirring frequently until it turns golden brown and develops a nutty aroma, about 5-7 minutes.

Mix the sugars: In a bowl, combine the browned butter with the powdered sugar and mix until well blended.

Combine dry ingredients: In a separate bowl, whisk together the all-purpose flour and salt.

Combine wet and dry: Gradually add the flour mixture to the butter mixture, stirring until a dough forms.

Add vanilla: Gently fold in the vanilla extract.

Shape the dough: Divide the dough in half and roll each portion into a log about 1.5 inches in diameter. Wrap each log in plastic wrap and refrigerate for at least one hour.

Preheat oven to 350°F (175°C) and line a baking sheet with parchment paper.

Slice the chilled dough logs into 1/4-inch thick rounds and place them on the prepared baking sheet.

Bake for 12-15 minutes, or until the edges are lightly golden.