Mix cocoa, sugar, and oil in a large bowl.
Beat in eggs one at a time, then vanilla.
Whisk flour, baking powder, and salt separately; gradually stir into chocolate mixture until just combined.
Cover; refrigerate at least 3 hours or overnight until firm.
Heat oven to 350°F; line sheets with parchment.
Put powdered sugar in a small bowl. Roll chilled dough into 1-inch balls; coat generously and completely in sugar.
Place 2 inches apart on sheets; bake 10-12 minutes until spread and cracked.
Cool on sheets 5 minutes, then on a rack; cookies firm as they cool.