Sift the cocoa powder into a small bowl to remove any lumps, which ensures smooth, lump-free cookies. In another bowl, whisk together flour, baking powder, and salt, breaking up any clumps in the brown sugar as you measure it. Have all ingredients measured and ready before you begin mixing, as the wet ingredients will come together quickly once you start.
In a large bowl, combine cocoa powder, granulated sugar, brown sugar, canola oil, and vanilla extract. Beat with an electric mixer for about 1-2 minutes until the mixture is well combined and slightly fluffy. The oil and sugars should emulsify slightly, creating a rich base that will help the cookies develop their signature crinkled texture.
Add eggs to the chocolate mixture one at a time, beating well after each addition for about 30 seconds. This gradual incorporation helps emulsify the eggs into the mixture rather than creating a separated, broken texture. Room temperature eggs combine more smoothly, so take them out of the fridge about 15 minutes before you start if you remember—but don't stress if you forget; they'll still work fine.
Add the dry ingredient mixture from Step 1 to the wet chocolate-egg mixture and fold together with a spatula until just combined, being careful not to overmix. Overmixing develops too much gluten, which makes cookies tough instead of tender. The dough should come together in a thick, fudgy consistency.
Cover the dough tightly with plastic wrap and refrigerate for at least 3 hours, or up to overnight. The chill time allows the flavors to develop and makes the dough easier to scoop without spreading. You can prepare this the night before if you'd like, making the baking day much quicker.
Preheat oven to 350°F and line two baking sheets with parchment paper. While the oven heats, place 1/4 cup granulated sugar in one shallow bowl and 1/2 cup powdered sugar in another shallow bowl. This two-sugar coating technique is what creates the signature crinkled appearance—the granulated sugar helps with the initial texture while the powdered sugar develops cracks as the cookie bakes and spreads.
Remove chilled dough from refrigerator and scoop 1-inch balls using a cookie scoop or tablespoon, working quickly so the dough doesn't warm up too much. Roll each ball first in granulated sugar, then immediately in powdered sugar, coating all sides. Place coated balls 2 inches apart on prepared baking sheets and bake for 10-12 minutes until the edges are set but the centers still look slightly underbaked and crackled. Let cookies cool on the baking sheet for 10-15 minutes before transferring to a wire rack—this cooling time allows the centers to set up properly so they stay fudgy rather than becoming cake-like.