In a large bowl, whisk together the granulated sugar and vegetable oil until combined. Add the eggs, one at a time, whisking well after each addition. Stir in the vanilla extract. This mixture will be smooth and slightly thick.
In a separate bowl, sift together the all-purpose flour, unsweetened cocoa powder, baking powder, and salt. Make sure there are no lumps for even mixing.
Gradually add the dry ingredients to the wet ingredients, stirring gently with a spatula until just combined. Avoid overmixing; it’s okay if a few streaks of flour remain. The dough will be sticky and thick.
Cover the dough with plastic wrap and refrigerate for at least 1 hour. Chilling helps the dough firm up, making it easier to handle and preventing excessive spreading.
Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper. Using a cookie scoop or spoon, scoop out about 1.5 tablespoon-sized portions of dough. Roll each portion into a ball, then roll it generously in powdered sugar until fully coated.
Place the rolled dough balls on the prepared baking sheet, spacing them about 2 inches apart. Bake for 10-12 minutes, or until the cookies have cracked beautifully on top but still feel soft in the center.
Remove the cookies from the oven and allow them to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely. The cookies will firm up slightly as they cool but remain soft and tender inside.