Preheat oven to 375°F. Line two cookie sheets with parchment paper.
Mix butter, 1/2 cup powdered sugar, and vanilla with an electric mixer until fluffy. Add flour and salt and mix until the dough comes together. Stir in the chocolate chips. If dough is too soft, chill it until you can work it easily with your hands.
Scoop 1 tablespoon balls of dough and place on prepared cookie sheet.
Bake cookies for 7-10 minutes until bottoms are just slightly brown. Remove from oven and cool for just a minute, until you can handle them. Fill a small bowl with powdered sugar and roll each cookie in the sugar until coated. Place on a rack to cool. (Once cookies are cooled, you may want to re-roll them in more powdered sugar.)