Preheat the oven to 350 F.
To clarify the butter: Place the unsalted butter in a medium pot over low heat, until it is melted.
Let it simmer until the foam goes to the top of the melted butter.
Remove the pan from the heat and let stand for about 5 minutes.
Skim the foam from the top and discard. Pour it into a bowl using a fine mesh strainer.
With an electric mixer, beat the butter for about 3 minutes. Add the sugar,vanilla and beat until well blended. Add the flour, and continue beating for 2 minutes.
Form the dough into a ball. Wrap in plastic and place in the fridge for about 30 minutes.
Roll 2 tablespoons of dough between your palms into balls. Place the balls on a large greased baking sheet about ½-inch apart. Flatten the balls using your hands.
Bake the cookies until golden on top, about 15 minutes. Let them cool for about 5 minutes on the baking sheet. Dust the cookies with the powdered sugar.