Whisk together flour, baking powder, and salt in a small bowl and set aside. In a large mixing bowl or stand mixer, combine cocoa powder, sugar, and vegetable oil, mixing until the cocoa is fully incorporated and the mixture resembles wet sand. Add the room-temperature eggs one at a time, beating well after each addition to ensure they're fully incorporated, then mix in vanilla extract. Gently fold in the dry ingredient mixture until just combined—don't overmix, as this keeps the cookies tender. Cover the dough with plastic wrap and refrigerate for at least 4 hours (or overnight). I find that chilling the dough is essential here; it prevents the cookies from spreading too much in the oven and helps them develop those beautiful crinkles.
Preheat your oven to 350°F and line a baking sheet with parchment paper. Pour the rainbow sprinkles into a shallow bowl and set it near your work station. This setup ensures everything is ready when you start shaping the dough, so you won't have cookies sitting out and warming up while you hunt for supplies.
Remove the chilled dough from the refrigerator and work quickly to prevent it from warming up too much. Scoop out 1-inch balls of dough using a small cookie scoop or your hands, then immediately roll each ball in the sprinkles until fully coated on all sides. The dough should be cold enough to hold its shape but still pliable—if it gets too warm, pop it back in the fridge for 10 minutes. Place the coated balls about 2 inches apart on the prepared baking sheet. I like to work in batches and keep the remaining dough in the fridge while I'm shaping, which prevents any spreading before baking.
Bake the cookies for 10-12 minutes at 350°F, until the tops look set and slightly cracked but the centers are still soft—they should look slightly underbaked when you pull them out. Let the cookies cool on the baking sheet for 5 minutes to firm up slightly, then transfer them to a wire rack to cool completely. The cookies will continue to set as they cool, creating that signature crinkly texture with a fudgy center.