In a large bowl, mix sugar, cocoa powder, and oil with a hand or stand mixer until smooth and shiny.
Beat in eggs one at a time, then add vanilla and mix well.
In another bowl, combine flour, baking powder, and salt. Gradually add to the cocoa mixture and mix on low until just combined.
Cover the dough with plastic wrap and refrigerate for at least 4 hours or overnight.
Preheat oven to 350°F and line baking sheets with parchment paper. Place powdered sugar in a small bowl.
Scoop chilled dough into 1-inch balls, roll them in powdered sugar, and place 2 inches apart on the baking sheet.
Bake for 10–12 minutes until edges are firm but centers are puffed and slightly wet.
Let cookies cool on the sheet for a few minutes, then transfer to a wire rack to cool completely.