Whisk the flour, cocoa powder, baking powder and salt in a medium bowl.
In a large bowl, whisk the granulated sugar, brown sugar, vegetable oil, eggs and vanilla until smooth and glossy.
Stir the dry mixture into the wet mixture with a spatula until no dry streaks remain. Cover and refrigerate for 30 minutes, until the dough is firm enough to scoop.
Heat the oven to 350°F. Line two baking sheets with parchment paper. Put the powdered sugar in a shallow bowl.
Scoop level 1-tablespoon portions of dough, roll into balls, and roll each ball in powdered sugar twice for a thick coat. Set 2 inches apart on the prepared sheets.
Bake both sheets at once for 11-12 minutes, rotating top to bottom and front to back halfway through, until the edges are set and the tops are crackled. The centers should still feel soft.
Cool on the sheets for 5 minutes, then transfer to a wire rack to cool completely. Store in an airtight container for up to 4 days.
