In a large mixing bowl, use a hand mixer or a stand mixer fitted with the paddle attachment to beat the sugar, cocoa powder, and oil together on medium speed until well combined and glossy.
Add the eggs one at a time, mixing thoroughly after each addition, then mix in the vanilla extract.
In a separate medium bowl, stir together the flour, baking powder, and salt.
Gradually add this flour mixture to the cocoa mixture, mixing on low speed just until everything is combined.
Wrap the dough in plastic and refrigerate it for at least 4 hours or overnight.
When ready to bake, preheat your oven to 350°F and line two baking sheets with parchment paper.
Put the powdered sugar into a small bowl.
Using a small scoop or tablespoon, scoop the chilled dough and roll it into one-inch balls, then coat each ball in powdered sugar and space them 2 inches apart on the baking sheets.
Only prepare as many as fit on your sheets, keeping the remaining dough refrigerated until ready to use.
Bake for 10–12 minutes, or until the edges are set and the centers are puffed but slightly glossy.
Cool the cookies on the baking sheet for a few minutes, then move them to a wire rack to cool completely.