In a large bowl, whisk the granulated sugar, oil, eggs and vanilla until smooth and glossy, about 1 minute.
Whisk the flour, cocoa powder, baking powder and salt in a medium bowl, then add to the wet ingredients and stir with a spatula until a soft, sticky dough forms.
Cover and refrigerate at least 2 hours (or up to overnight), until the dough is firm enough to roll.
Heat the oven to 350°F and line two baking sheets with parchment paper.
Put the powdered sugar in a small bowl. Roll the dough into 1-inch balls, roll each generously in powdered sugar until fully coated, and place 2 inches apart on the baking sheets.
Bake 10-12 minutes, until the tops crack and the edges are set but the centers still look soft.
Cool on the baking sheet 5 minutes, then transfer to a wire rack to cool completely.
