In a small bowl, add the flour, cocoa, baking powder, and salt and whisk to combine. Set aside.
In a medium bowl or the bowl of a stand mixer, add the oil and both sugars and beat together on medium-low speed until fully combined (it will probably look something like wet sand, this is ok!) Add the vanilla and then the eggs, one at a time and beating the mix together until smooth between each one.
Slowly sift the dry ingredients into the wet ingredients, pausing a few times to mix everything together on low speed. Scrape down the sides as necessary. It will be quite thick, like a very thick brownie batter (because that's pretty much what crinkle cookies are!) Once all the dry ingredients have been added and everything is mixed together, cover the bowl with plastic wrap and chill for at least 2 hours, or overnight. If chilling for longer than 2 hours, leave the dough out to warm up for ~15 minutes before baking.
When ready to bake, preheat the oven to 350°F. Line a baking sheet with parchment paper and set aside. In a small bowl or dish, add the powdered sugar. Using a spoon or a cookie scoop, scoop out ~1-1.5 tbsp sized balls of dough, and roll together into a ball in your hands. The dough will still be quite sticky, so I recommend dusting your hands with powdered sugar before. Once you've formed a ball, roll the dough in the powdered sugar to completely coat it. You want a nice thick layer! Once coated, place on the baking sheet and repeat with the rest of the dough. They will spread a bit, so leave ~1-2" between cookies.
Bake the cookies for 10-12 minutes, they should be barely set to the touch, as they will firm up once out of the oven. Remove the baking sheet from the oven and gently but firmly tap it on the counter a few times. Let the cookies cool for a few minutes on the baking sheet before transferring to a wire rack to cool.
Enjoy!
