In a medium bowl, whisk together the flour, cocoa powder, baking powder, and salt until no cocoa lumps remain. Set aside.

In a large bowl, whisk the granulated sugar and oil until combined. Add the melted chocolate and whisk until smooth. Add the eggs one at a time, whisking well after each, then stir in the vanilla. The mixture will look glossy and thick.

Add the dry ingredients to the wet and stir with a wooden spoon or spatula until just combined and no streaks of flour remain. The dough will be soft and sticky, more like thick brownie batter than typical cookie dough.

Cover the bowl tightly and refrigerate for at least 3 hours, or up to overnight. The dough must be cold and firm enough to scoop and shape. Do not skip this step or the cookies will spread flat and the crinkle effect will fail.

Preheat oven to 350 degrees F. Line baking sheets with parchment paper. Place the powdered sugar in a shallow bowl.

Scoop rounded tablespoons of cold dough and roll quickly between your palms into 1-inch balls. Roll each ball generously in powdered sugar until completely coated - do not shake off excess. The thick layer of sugar creates the dramatic crackle.

Place balls 2 inches apart on prepared sheets. Bake for 10-12 minutes until the cookies have puffed, cracked, and the edges look set but centers are still slightly soft. They will look underdone in the middle - this is correct.

Cool on the baking sheet for 5 minutes, then transfer to wire racks to cool completely. The cookies will fall slightly and develop their characteristic fudgy centers as they cool.