In a large mixing bowl, combine the granulated sugar and vegetable oil. Stir until well blended, then mix in the cocoa powder.
Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.
In a separate bowl, whisk together the flour, cocoa powder, baking powder, and salt.
Add the dry ingredients to the wet ingredients and stir until fully combined and smooth.
Cover the bowl and refrigerate for at least 4 hours, or up to overnight.
When ready to bake, preheat the oven to 350 degrees F. Line a baking sheet with parchment paper or a silicone baking mat.
Place the powdered sugar in a shallow bowl.
Scoop and roll the chilled dough into balls, then coat generously in powdered sugar.
Arrange the dough balls on the prepared baking sheet, leaving about 2 inches of space between each.
Bake for 11 to 13 minutes, until the cookies are set and crinkled.
Let the cookies cool on the baking sheet for a few minutes before transferring to a wire rack to cool completely.
Store in an airtight container once cooled.