Giant, cakey, and wonderful!
Preheat your oven to 375F and line one or two large baking sheets with parchment paper.If you only have one sheet, don't worry because the cookies need to be baked in batches anyways, you'll just have to wait a little longer.
In a large bowl, add the flour, 1/4 of powdered sugar, salt, baking powder and baking soda. Stir well to combine.
In a separate large or medium bowl, add the sugar, coconut oil, milk and vanilla extract. Using a hand mixer, beat on low until it is well combined. There's too much milk for it to become completely smooth but the coconut oil will break down considerably. Once done, add this mix to the dry and beat on low until just combined, stopping to fold together the mixture if some dry bits stick out. Please do not overmix.
With clean but dry (or very slightly damp) hands (you don't want to add extra moisture to this if you don't have to) scoop up a large amount of dough, almost the size of your palm, and roll into a ball. Place on the baking sheet, away from any corners and flatten with the side of your hand. You don't want them to be super thin, but around 1/2 inch thick. See the photo above if you need clarification on this. The cookies will for the most part retain the shape you given them here, they will just get spread so keep that in mind. If you want perfect round cookies I would suggest flattening them and then using a cup or bowl to cut off the excess edges.
You will likely only be able to get 3-4 cookies on a sheet at a time and please give them lots of room to cook properly. Place in the oven and bake for 10-11 minutes. Ideally, you want the bottoms to be slightly golden, to know they're done. Once removed, let them cool on the same sheet for at east 15 minutes then transfer to a cooling rack to cool completely.
If you have a second baking sheet ready, repeat all the same steps, or wait until the first batch is on the cooling rack and again, repeat.
In a medium (or large) bowl, add 1 1/2 cups of the powdered sugar, 1 tablespoon of coconut oil, 2 tablespoons non-dairy milk, and a pinch of salt. Beat on low until well combined. You don't want it to be drippy wet, but not completely stiff either. Easy to spread but still thin. If you find it's too dry add in extra non-dairy milk, starting with 1 teaspoon. If it's too wet, add in some more powdered sugar, 2 teaspoons at a time, then beat again until smooth. This will be the white icing.
In a separate medium (or large) bowl, add the other 1 1/2 cups powdered sugar, cocoa powder, 1 tablespoon of coconut oil, 3 tablespoons non-dairy milk, a pinch of salt and the optional vanilla, if using. Once again, beat until just combined. Add in more milk, or powdered sugar as needed. This will be the black icing.
Make sure the cookies are completely cool before you decorate them as all the icing will just run off. It doesn't matter which side you decorate. Using a knife or spoon, coat one half with white icing. This will be messy so you may want to put paper towel under the cooling rack. It's best over the cooling rack so the excess can drip off, making for a cleaner cookie. Repeat for the rest of the cookies, decorating only one colour at a time.
Once the first half is dry, repeat with the black icing, doing your best not to go over the white. If you do, don't fret as you can cover those patches up with more icing
If you did by chance decorate the cookies too early, or the white side looks too thin, add another coat prior to adding the black icing. You should have plenty of icing, with extra, but if not, you can make a half batch more.
Once the last side is dry, serve! These are best day of but still good for 2 days after. The only thing is the icing can dry out so it's best to decorate them the day of eating.