Preheat the oven to 350°F. Line baking sheets with parchment paper or a silicone baking mat.
In a large bowl, beat together the sugar, butter and vanilla until light and fluffy. Add in the eggs one at a time, beating well after each addition.
Mix in the baking soda. Add in the flour, and mix until fully incorporated.
Place the powdered sugar in a small bowl. Roll the dough into balls, and roll the balls in the powdered sugar until fully coated. Place the balls on the prepared baking sheets.
Bake in the preheated oven for 12 minutes, or until the cookies have spread and cracked on top. Allow to cool on the baking sheets for 5 minutes, then transfer to wire racks to cool completely.