Preheat your oven to 350°F (175°C) and prepare two baking sheets by lining them with parchment paper.
Using an electric mixer, beat together the softened butter, ½ cup of powdered sugar, cocoa powder, and vanilla until the mixture becomes light and fluffy.
Gradually mix in the flour and salt, continuing until a dough forms. Gently fold in the chocolate chips. If the dough feels too soft, chill it in the refrigerator until it's firm enough to handle.
Scoop out tablespoon-sized portions of dough and shape them into small balls. Arrange them on the prepared baking sheets.
Bake the cookies for 7 to 10 minutes, until the bottoms show a light golden hue and the tops lose their glossy appearance. Remove from the oven and let them cool for about 5-10 minutes, until they are easy to handle.
Pour 1 cup of powdered sugar into a small bowl. Roll each cookie in the powdered sugar until they are thoroughly coated, then transfer them to a cooling rack. Once the cookies have fully cooled, you may want to roll them again in additional powdered sugar for a thicker coating.