In a medium bowl, combine the granulated sugar with the oil until well combined. Add the eggs and vanilla and whisk together for 1 minute until smooth.
Sift the flour, cacao powder, baking powder, and salt in a second bowl. Add the flour mixture to the egg mixture and mix [with a spoon] until well combined. Continue to mix the ingredients, by hand, for 1 minute to ensure all ingredients are well incorporated.
Cover the bowl with the batter and place it in your fridge to chill for 1-2 hours or overnight.
Preheat oven to 350º F and prepare a baking sheet with a piece of parchment paper or silicone baking mat. Place the powdered sugar in a small bowl and set aside.
Roll the dough into 12 evenly-sized rounded balls (about 1" to 1.5" balls). Lightly wet your hands to prevent the dough from sticking to them. You could also use a cookie scooper to help shape the dough. Place each dough ball on a piece of plastic wrap.
Roll each dough ball in the powdered sugar and then place each cookie on your baking sheet 1-1.5 inches apart. Do not flatten the dough. The cookies will spread.
Bake for 9-10 minutes, then remove the cookies from the oven and allow them to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.
Serve immediately or store in a sealed container for 3-4 days at room temperature.
Notes
Flour: I've only tested this flour with Bob's Red Mill 1-to-1 Gluten-Free Flour Blend. If you use another flour blend, make sure it includes xanthan gum, an essential binder in gluten-free baking, or add 1/2 tsp of it. Without xanthan gum, the cookies would literally crumble!Dairy-Free: This recipe is dairy free. Cacao powder contains no dairy. Cocoa powder is typically gluten free, although some brands add milk. Read ingredient labels carefully. I recommend Navitas cacao powder.Egg-Free: I have not tested this recipe without eggs, but if you try it, I recommend using 2 flax eggs. To make each flax egg, combine 1 tbsp flaxseed + 3 tbsp warm water and allow it to sit for five minutes until it forms a gel. Remember to double the recipe, as the recipe calls for two eggs.Cacao Powder: I recommend using cacao powder to give these gluten-free crinkle cookies their chocolate flavor. You could use cocoa powder instead of cacao powder, but please note that cacao powder absorbs less liquid than cocoa powder, so when using cocoa powder, you may want to add a bit more oil to the mixture.Vegetable Oil: Choose a neutral-tasting vegetable oil, like avocado oil (which is what I use), canola oil, grapeseed oil, or sunflower oil. Powdered Sugar: Powdered sugar, also known as icing sugar and confectioner's sugar, is a must in this recipe as it adds a beautiful snow-like coating to the cookies. If you're looking to avoid corn products, please note that most powdered sugar contains cornstarch. You can, however, find powdered sugar made with tapioca starch.