In a medium bowl, whisk together the flour, cocoa powder, baking powder, and salt. Set aside.

In a large bowl, using an electric mixer, beat the 1 cup granulated sugar and vegetable oil on medium speed until well combined, about 1-2 minutes. Beat in the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.

Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined and no streaks of flour remain. Do not overmix. The dough will be thick and sticky.

Cover the bowl with plastic wrap and refrigerate for at least 2 hours, or up to overnight. Chilling is crucial for the dough to firm up and for the cookies to hold their shape and crinkle properly.

Preheat your oven to 350°F (175°C). Line two baking sheets with parchment paper.

Place the 1/2 cup granulated sugar in one small bowl and the 1 cup powdered sugar in another small bowl.

Scoop out tablespoon-sized portions of the chilled dough. Roll each portion into a ball. First, roll each dough ball in the granulated sugar, ensuring it's fully coated. Then, roll it generously in the powdered sugar, making sure it's completely covered. The thicker the powdered sugar coating, the more pronounced the crinkles will be.

Place the coated dough balls about 2 inches apart on the prepared baking sheets.

Bake for 10-12 minutes, or until the edges are set and the centers are still slightly soft. Do not overbake. The powdered sugar coating should remain white and cracked.

Remove the baking sheets from the oven and let the cookies cool on the sheets for 5 minutes before transferring them to a wire rack to cool completely.