In a medium bowl, whisk together the all-purpose flour, unsweetened cocoa powder, baking powder, and salt until evenly combined.
In a large bowl, whisk the granulated sugar, eggs, vegetable oil, and vanilla extract until smooth and slightly thick, 1–2 minutes.
Add the dry mixture to the wet mixture and stir with a spatula just until no dry streaks remain; the dough will be sticky.
Cover the bowl and chill until the dough is firm enough to scoop, 2–3 hours (or up to overnight).
Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper.
Place the confectioners' sugar in a shallow bowl for coating.
Working with about 1 tablespoon of dough per cookie, scoop and roll into balls between your palms. Roll each ball generously in the confectioners' sugar until thickly coated and place on the prepared sheets, spacing about 2 inches apart.
Bake one sheet at a time until the cookies are puffed with pronounced cracks and the edges are just set but centers are still soft, 10–12 minutes, rotating the pan halfway through.
Let the cookies cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely. Keep the remaining dough chilled between batches for best crinkles.
Serve once cool; store airtight at room temperature for up to 4 days.