Combine the sugar, cocoa powder and oil. Beat on medium speed until well-combined and shiny. Add the eggs one at a time, beating until well combined. Beat in the vanilla.
Combine the flour, baking powder and salt in a medium bowl, stirring to combine. Add the flour mixture to the cocoa mixture and mix on low speed just until combined. Cover the dough in plastic wrap and refrigerate for at least 4 hours (or overnight).
Once the dough has chilled, preheat oven to 350 F. Line two large baking sheets with parchment paper. Place the powdered sugar in a small bowl.
Using a small ice cream scoop or tablespoon, scoop the chilled dough and roll into roughly one-inch balls. Roll the dough balls in powdered sugar until well coated and place on the prepared baking sheet about 2 inches apart. Do not work ahead; keep dough chilled until using.
Bake for 10 to 12 minutes or until the edges of the cookies are firm and the center is puffed but still appears slightly wet.
Let them cool on the baking sheets for a few minutes, and then transfer to a wire rack to cool completely.
