Preheat your oven to 350°F (175°C). Line baking sheets with parchment paper.
In a mixing bowl, combine granulated sugar, cocoa powder, and vegetable oil. Mix until well combined.
Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
In another bowl, whisk together all-purpose flour, baking powder, and salt. Gradually add this dry mixture to the wet ingredients, mixing until just incorporated. The dough will be thick.
Chill the dough in the refrigerator for about 30 minutes for easier handling.
Once chilled, scoop tablespoon-sized portions of dough and roll them into balls. Roll each ball in powdered sugar until fully coated.
Place the coated dough balls on prepared baking sheets, spacing them about 2 inches apart.
Bake in the preheated oven for 10-12 minutes. The cookies will puff up and then crack on top.
Remove from the oven and let the cookies cool on the baking sheet for about 5 minutes before transferring them to a cooling rack to cool completely.